Multi-core optical fiber and multi-core optical fiber cable

ABSTRACT

This MCF ensures sufficient manufacturing tolerance, is excellent in mass productivity, and is also capable of suppressing degradation of splice loss. The MCF includes four cores and a common cladding. Each core has adjacent relationships with two cores of remaining cores, an adjacent core interval Λ is from Λnominal−0.9 μm to Λnominal+0.9 μm, a common cladding diameter is from 124 μm to 126 μm, an MFD, λcc and dcoat at a wavelength of 1310 nm satisfy a predetermined relationship, the MFD is from a MFD-reference-value−0.4 μm to the MFD-reference-value+0.4 μm with the MFD-reference-value of from 8.6 μm to 9.2 μm, a zero-dispersion wavelength is from a wavelength-reference-value−12 nm to the wavelength-reference-value+12 nm with the wavelength-reference-value of from 1312 nm to 1340 nm, a dispersion slope at a zero-dispersion wavelength is 0.092 ps/(nm2·km) or less, λcc is 1260 nm or less, and a predetermined structural condition and an optical condition are satisfied.

TECHNICAL FIELD

The present disclosure relates to a multi-core optical fiber(hereinafter, referred to as an “MCF”) and a multi-core optical fibercable (hereinafter, referred to as an “MCF cable”).

The present application claims priority from Japanese Patent ApplicationNo. 2020-174958 filed on Oct. 16, 2020, which is based on the contentsand all of which are incorporated herein by reference in their entirety.

BACKGROUND

Non-Patent Document 1 discloses a trench-assisted four-core fiberincluding four cores, and a cladding having an outer diameter of 125 μm.The depth of the trench is approximately −0.7% or less. A mode fielddiameter (hereinafter, referred to as an “MFD”) at a wavelength of 1310nm is 8.4 μm or more and 8.6 μm or less. The cable cutoff wavelength is1171 nm or more and 1195 nm or less. The zero-dispersion wavelength is1317 nm or more and 1319 nm or less. The wavelength dispersion slope atthe zero-dispersion wavelength is 0.090 ps/(nm²·km) or more and 0.091ps/(nm²·km) or less. In addition, the transmission loss is 0.33 dB/km ormore and 0.35 dB/km or less at the wavelength of 1310 nm, and 0.19 dB/kmor more and 0.21 dB/km or less at a wavelength of 1550 nm. A crosstalk(hereinafter, referred to as an “XT”) between cores at a wavelength of1625 nm is −43 dB/km.

Non-Patent Document 2 discloses a trenchless four-core fiber includingfour cores, and a cladding having an outer diameter of 125 μm. The MFDis 8.6 μm or more and 8.8 μm or less at the wavelength of 1310 nm, andis 9.6 μm or more and 9.8 μm or less at the wavelength of 1550 nm. Thecable cutoff wavelength is 1234 nm or more and 1244 nm or less. Thezero-dispersion wavelength is 1318 nm or more and 1322 nm or less. Thewavelength dispersion slope at the zero-dispersion wavelength is 0.088ps/(nm²·km) or less and 0.089 ps/(nm²·km) or less. A transmission lossat the wavelength of 1310 nm is 0.328 dB/km or more and 0.330 dB/km orless, a transmission loss at a wavelength of 1550 nm is 0.188 dB/km ormore and 0.193 dB/km or less, and a transmission loss at the wavelengthof 1625 nm is 0.233 dB/km or more and 0.245 dB/km or less. Theinter-core XT on an O-band (1260 nm or more and 1360 nm or less) is −56dB/km or less, and the inter-core XT on a C-band (1530 nm or more and1565 nm or less) is −30 dB/km or less. Note that MFD/λ_(cc) that hasbeen calculated from the values in Table.1 of Non-Patent Document 2 hasextremely small variations that are 6.97 or more and 7.08 or less.

Patent Document 1 discloses a trenchless four-core fiber including fourcores, and a cladding having the outer diameter of 125 μm. With a valueof 40 μm or more and 41.5 μm or less used as a pitch reference value, acore pitch (a distance between centers) falls within a range of a valueof the pitch reference value−1 μm or more and a value of the pitchreference value+1 μm or less. d_(coat) (a so-called OCT) falls within arange of 32 μm or more and 34 μm with 33 μm or less used as a basis. TheV value is 2.50 or more and 2.58 or less. The MFD at the wavelength of1310 nm is 8.0 μm or more and 8.3 μm or less. The bending loss at thewavelength of 1625 nm is 0.1 dB/100 turns or less at a bending radius 30mm. The effective cutoff wavelength (not defined) is 1260 nm or less.The zero-dispersion wavelength is 1300 nm or more and 1324 nm or less.The XT among the four cores after transmission for 10 km at thewavelength of 1550 nm is −30 dB or less.

Patent Document 2 discloses a trenchless four-core fiber including fourcores, and a cladding having an outer diameter of 125 μm, and theinter-core XT is suppressed to a certain value or less. Note that PatentDocument 2 does not disclose a method necessary for suppressing theinter-core XT to the certain value or less. That is, the upper limitvalue of the core pitch A for suppressing the leakage loss to thecoating is disclosed. However, the lower limit value of A necessary forsuppressing the inter-core XT is not disclosed. In addition, A forrealizing the XT of FIG. 6 of Patent Document 2 is not disclosed,either. Note that in paragraph “0026” of Patent Document 2, the upperlimit value of A is defined by Formula (3) (whereas in paragraph “0028”,the minimum value of A is defined by Formula (3), and the description isinconsistent).

-   Patent Document 1: Japanese Patent Application Laid-Open No.    2013-088458-   Patent Document 2: WO 2020/149158 A-   Patent Document 3: U.S. Pat. No. 9,933,331-   Non-Patent Document 1: Takashi Matsui, et al., “Design of 125 μm    cladding multi-core fiber with full-band compatibility to    conventional single-mode fiber,” Eur. Conf. Opt. Commun. (ECOC)    2015, the Internet-   <URL: https://doi.org/10.1109/ECOC.2015.7341966>.-   Non-Patent Document 2: T. Matsui et al., “Step-index profile    multi-core fibre with standard 125-μm cladding to full-band    application,” in Eur. Conf. Opt. Commun. (ECOC) (2019), the Internet-   <URL: https://doi.org/10.1049/cp.2019.0751>.-   Non-Patent Document 3: R. J. Black and C. Pask, J. Opt. Soc. Am. A,    JOSAA 1(11), p. 1129-1131, 1984.-   Non-Patent Document 4: T. Matsui et al., in Eur. Conf. Opt. Commun.    (ECOC2017), p. W.1.B.2.

SUMMARY

In order to solve the above-described problem, an MCF according to thepresent disclosure includes four cores extending along a central axis,and a common cladding. Each core has an adjacent relationship with twocores of remaining cores, a center-to-center interval Λ between thecores having the adjacent relationship falls within a range of a valueof Λ_(nominal)−0.9 μm or more and a value of Λ_(nominal)+0.9 μm or lesswith a nominal value Λ_(nominal) used as a basis, an outer diameter ofthe common cladding falls within a range of 124 μm or more and 126 μm orless with 125 μm used as a basis, in each core, an MFD, λ_(cc), andd_(coat) at a wavelength of 1310 nm satisfy a predeterminedrelationship, in each core, the MFD falls within a range of a value ofan MFD reference value−0.4 μm or more and a value of the MFD referencevalue+0.4 μm or less with a value of 8.6 μm or more and 9.2 μm or lessused as the MFD reference value, in each core, a zero-dispersionwavelength falls within a range of a value of a wavelength referencevalue−12 nm or more and a value of the wavelength reference value+12 nmor less with a value of 1312 nm or more and 1340 nm or less used as thewavelength reference value, in each core, a dispersion slope at thezero-dispersion wavelength is 0.092 ps/(nm²·km) or less, in each core,λ_(cc) is 1260 nm or less, and a predetermined structural condition anda predetermined optical condition are satisfied.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram illustrating various structures of an MCF cable(including an MCF according to the present disclosure) according to thepresent disclosure.

FIG. 2 is a diagram illustrating various core arrangements in the MCFaccording to the present disclosure.

FIG. 3 is a diagram for describing main terms used in the presentspecification.

FIG. 4 is a diagram illustrating a refractive index profile around eachcore applicable to the MCFs according to the present disclosure.

FIG. 5 is a graph illustrating a relationship between a center-to-centerinterval Λ between adjacent cores and MFD/λ_(cc) of a case where acounter propagation XT at a wavelength of 1360 nm after propagation for10 km (corresponding to a fiber length of 10 km) is −20 dB (=−20 dB/10km), in an MCF in which four cores are arranged to constitute a squarelattice (hereinafter, referred to as a “four-core MCF”).

FIG. 6 is a graph illustrating a relationship between thecenter-to-center interval Λ between the adjacent cores and MFD/λ_(cc) ofa case where the counter propagation XT after the propagation for 10 km(corresponding to the fiber length of 10 km) of the four-core MCF is −20dB and a case where parallel propagation XT after the propagation for 10km (corresponding to the fiber length of 10 km) of the four-core MCF is−20 dB, at both the wavelength of 1550 nm and the wavelength of 1360 nm.

FIG. 7 is a graph illustrating a relationship between thecenter-to-center interval Λ between the adjacent cores and MFD/λ_(cc) ofa case where the counter propagation XT after the propagation for 10 km(corresponding to the fiber length of 10 km) of the four-core MCF is −40dB and a case where the parallel propagation XT after the propagationfor 10 km (corresponding to the fiber length of 10 km) of the four-coreMCF is −40 dB, at both the wavelength of 1550 nm and the wavelength of1360 nm.

FIG. 8 is a graph illustrating a relationship between d_(coat) andMFD/λ_(cc) of a case where a leakage loss to the coating at thewavelength of 1360 nm is 0.01 dB/km, in the four-core MCF.

FIG. 9 is a graph illustrating a relationship between a CD (an allowableminimum cladding diameter) and MFD/λ_(cc) of a case where a margin of 1μm is added to d_(coat), when the leakage loss to the coating at thewavelength of 1360 nm is 0.01 dB/km, and the margin of 1 μm is added toA, when the counter propagation XT at the wavelength of 1360 nm afterthe propagation for 10 km (corresponding to the fiber length of 10 km)is −20 dB (=−20 dB/10 km), in the four-core MCF.

FIG. 10 is a graph illustrating a relationship between the CD (theallowable minimum cladding diameter) and MFD/λ_(cc) of a case where amargin of 1 μm is added to d_(coat) and the margin of 1 μm is added toΛ, when the leakage loss to the coating is 0.01 dB/km, under a conditionthat the counter propagation XT after the propagation for 10 km(corresponding to the fiber length of 10 km) of the four-core MCF is −20dB (=−20 dB/10 km) and the parallel propagation XT (an XT at generalpropagation in an identical direction) after the propagation for 10 km(corresponding to the fiber length of 10 km) is −20 dB (=−20 dB/10 km),at both the wavelength of 1550 nm and the wavelength of 1360 inn.

FIG. 11 is a graph illustrating a relationship between the CD (theallowable minimum cladding diameter) and MFD/λ_(cc) of a case where amargin of 1 μm is added to d_(coat) and the margin of 1 μm is added toA, when the leakage loss to the coating is 0.01 dB/km, under a conditionthat the counter propagation XT after the propagation for 10 km(corresponding to the fiber length of 10 km) of the four-core MCF is −40dB (=−40 dB/10 km) and the parallel propagation XT after the propagationfor 10 km (corresponding to the fiber length of 10 km) is −40 dB (=−40dB/10 km), at both the wavelength of 1550 nm and the wavelength of 1360nm.

DETAILED DESCRIPTION Problems to be Solved by the Present Disclosure

The inventor has studied the above-described conventional techniques andfound the following problems. That is, the MCF of the above Non-PatentDocument 1 is significantly worse in mass productivity than ageneral-purpose single mode fiber (hereinafter, referred to as an“SMF”), and the manufacturing cost becomes higher. This is because it isnecessary to provide a trench layer having a low refractive index thatis large in relative refractive index difference with respect to thecladding around each core in order to simultaneously achieve a reductionof the inter-core XT, an increase in the number of cores, a reduction inthe cladding outer diameter, and an increase in the MFD in each core.

Also with regard to the MCFs in the above Non-Patent Document 2, PatentDocument 1, and Patent Document 2, the manufacturing tolerance isnarrow, and the manufacturing cost increases. In a relatively shortdistance, an MCF usable from 1260 nm to 1625 nm is proposed. However,such an MCF is demanded to have optical characteristics in a designrange that cannot be achieved without controlling a refractive indexprofile with very high accuracy. Therefore, the manufacturing tolerancealmost the same as that of the general-purpose SMF cannot be achieved.

In addition, the presence or absence of a trench is not apparentlydisclosed in the above Patent Document 1, but it can be understood thata trench type is not practically included from the disclosed content (adefinition of a V value and a range of the V value). Even in a shortdistance, improvements in the transmission characteristics other than anO-band are also attempted. As a result, the manufacturing tolerance isnarrowed.

The present disclosure has been made to solve the problems as describedabove, and has an object to provide an MCF for short-distancetransmission, by which sufficient manufacturing tolerance is ensured,mass productivity is superior, and degradation in splice loss is alsosuppressed.

Descriptions of Embodiments of the Present Disclosure

First, contents in embodiments of the present disclosure will beindividually listed and described.

(1) According to one aspect of the present disclosure, a multi-coreoptical fiber (MCF) includes four cores extending along a central axis,and a common cladding covering each of the four cores. In particular,the four cores each have an adjacent relationship with two cores ofremaining cores. A center-to-center interval Λ between the cores havingthe adjacent relationship among the four cores falls within a range of avalue of Λ_(nominal)−0.9 μm or more and a value of Λ_(nominal)+0.9 μm orless with a predetermined core-interval nominal value Λ_(nominal) usedas a basis. An outer diameter of the common cladding falls within arange of 124 μm or more and 126 μm or less with 125 μm used as a basis.In each of the four cores, an MFD at a wavelength of 1310 nm, a cablecutoff wavelength λ_(cc) measured on a 22 in length of fiber, and ashortest distance d_(coat) of distances from centers of the four coresto an outer periphery of the common cladding satisfy a relationship in afollowing Formula (1):

d _(coat)≥2.88MFD/λ_(cc)+5.36  (1).

Further, in each of the four cores, the MFD falls within a range of avalue of an MFD reference value−0.4 μm or more and a value of the MFDreference value+0.4 μm or less with a value of 8.6 μm or more and 9.2 μmor less used as the MFD reference value. In each of the four cores, azero-dispersion wavelength falls within a range of a value of awavelength reference value−12 nm or more and a value of the wavelengthreference value+12 nm or less with a value of 1312 nm or more and 1340nm or less used as the wavelength reference value. In each of the fourcores, a dispersion slope at the zero-dispersion wavelength is 0.092ps/(nm²·km) or less. In each of the four cores, the cutoff wavelengthλ_(cc) is 1260 nm or less. Further, the MCF satisfies either a firstcondition or a second condition in the following, and satisfies either athird condition or a fourth condition in the following.

The first condition is defined that each of the four cores is in directcontact with the common cladding. The second condition relates to eachof the four cores, each of the four cores further including an opticalcladding provided between each the four cores and the common cladding,and is defined that a relative refractive index difference Δ2 of theoptical cladding with respect to the common cladding satisfies arelationship that −0.1%≤Δ2≤0.1%.

The third condition is defined that an XT between the cores having theadjacent relationship for a fiber length of 10 km at a wavelength of1360 nm is −10 dB or less, and in each of the four cores, MFD/λ_(cc) anda center-to-center interval Λ_(a) between the cores having the adjacentrelationship satisfy any one of following Formula (2) to Formula (6):

7.2≤MFD/λ_(cc)≤8.2≤0.443Λ_(a)−5.33  (2);

7.2≤MFD/λ_(cc)≤8.7≤0.443Λ_(a)−5.33  (3);

7.2≤MFD/λ_(cc)≤9.2≤0.443Λ_(a)−5.33  (4);

7.2≤MFD/λ_(cc)≤9.7≤0.443Λ_(a)−5.33  (5); and

7.2≤MFD/λ_(cc)≤10.2≤0.443Λ_(a)−5.33  (6).

The fourth condition is defined that the XT between the cores having theadjacent relationship for the fiber length of 10 km at the wavelength of1360 nm is −20 dB or less, and in each of the four cores, MFD/λ_(cc) andthe center-to-center interval Λ_(a) between the cores having theadjacent relationship satisfy any one of the following Formula (7) toFormula (11):

7.2≤MFD/λ_(cc)≤8.2≤0.392Λ_(a)−4.88  (7);

7.2≤MFD/λ_(cc)≤8.7≤0.392Λ_(a)−4.88  (8);

7.2≤MFD/λ_(cc)≤9.2≤0.392Λ_(a)−4.88  (9);

7.2≤MFD/λ_(cc)≤9.7≤0.392Λ_(a)−4.88  (10); and

7.2≤MFD/λ_(cc)≤10.2≤0.392Λ_(a)−4.88  (11).

The MCF having the above-described structure is a four-core fiberarranged in a square and having a standard cladding diameter, and hasoptical characteristics suited for an O band while ensuring sufficienttolerance in mass production. In addition, the outer diameter of thecommon cladding falls within the range of 124 μm or more and 126 μm orless with 125 μm used as a basis. Thus, the leakage loss from theoutermost peripheral core to the coating at the wavelength of 1360 nm issuppressed to 0.01 dB/km or less. Further, in a case where the MCFsatisfies the above third condition, the tolerance of MFD/λ_(cc) canalso be ensured, and the total amount of the counter propagation XT to apredetermined core for the fiber length of 10 km at the wavelength of1360 nm or less can be suppressed to −20 dB or less with a high yield atthe time of fiber mass production. In a case where the MCF satisfies theabove fourth condition, the tolerance of MFD/λ_(cc) can also be ensured,and the total amount of the counter propagation XT to the predeterminedcore for the fiber length of 10 km at the wavelength of 1360 nm or lesscan be suppressed to −40 dB or less with a high yield at the time offiber mass production. The “leakage loss” can be calculated by themethod described in the above Patent Document 3, and the disclosedcontent thereof is incorporated herein by reference to Patent Document3.

(2) According to one aspect of the present disclosure, the MCF includesfour cores extending along a central axis, and a common claddingcovering each of the four cores. The four cores each have an adjacentrelationship with two cores of remaining cores. A center-to-centerinterval Λ between adjacent cores among the four cores falls within arange of a value of A nominal −0.9 μm or more and a value of Λnominal+0.9 μm or less with a predetermined core interval nominal valueΛ nominal as a basis. A diameter CD of the common cladding falls withina range of a value of CD_(nominal)−1 μm or more and a value ofCD_(nominal)+1 lam or less with a predetermined cladding diameternominal value CD_(nominal) [μm] of less than 125 μm used as a basis. Ineach of the four cores, an MFD at a wavelength of 1310 nm and a cablecutoff wavelength λ_(cc) measured on a 22 in length of fiber satisfy afollowing Formula (12):

d _(coat)≥2.88MFD/λ_(cc)+5.36  (12).

In each of the four cores, the MFD falls within a range of a value of anMFD reference value−0.4 μm or more and a value of the MFD referencevalue+0.4 μm or less with a value of 8.6 μm or more and 9.2 μm or lessused as the MFD reference value. The MCF according to the presentdisclosure preferably has a zero-dispersion wavelength that falls withina range of a value of the wavelength reference value−12 nm or more and avalue of the wavelength reference value+12 nm or less, with apredetermined value uses as a wavelength reference value of 1312 nm ormore and 1340 nm or less. In each of the four cores, a dispersion slopeat the zero-dispersion wavelength is 0.092 ps/(nm²·km) or less. In eachof the four cores, the cutoff wavelength A is 1260 nm or less. Further,the MCF satisfies either a first condition or a second condition in thefollowing, and satisfies either a fifth condition or a sixth conditionin the following.

The first condition is defined that each of the four cores is in directcontact with the common cladding. The second condition relates to eachof the four cores, each of the four cores further including an opticalcladding provided between each the four cores and the common cladding,and is defined that a relative refractive index difference Δ2 of theoptical cladding with respect to the common cladding satisfies arelationship that −0.1%≤Δ2≤0.1%.

The fifth condition is defined that an XT between the cores having theadjacent relationship for a fiber length of 10 km at a wavelength of1360 nm is −10 dB or less, in each of the four cores, the followingFormula (13):

CD _(nominal)≥13.31MFD/λ_(cc)+24.47  (13)

is satisfied,

and in each of the four cores, MFD/λ_(cc) and a center-to-centerinterval Λ_(a) between the cores having the adjacent relationshipsatisfy any one of the following Formula (14) to Formula (18):

6.5≤MFD/λ_(cc)≤7.5≤0.443Λ_(a)−5.33  (14);

6.5≤MFD/λ_(cc)≤8.0≤0.443Λ_(a)−5.33  (15);

6.5≤MFD/λ_(cc)≤8.5≤0.443Λ_(a)−5.33  (16);

6.5≤MFD/λ_(cc)≤9.0≤0.443Λ_(a)−5.33  (17); and

6.5≤MFD/λ_(cc)≤9.5≤0.443Λ_(a)−5.33  (18).

The sixth condition is defined that the XT between the cores having theadjacent relationship at the wavelength of 1360 nm for the fiber lengthof 10 km is −20 dB or less, in each of the four cores, the followingFormula (19):

CD _(nominal)≤9.37MFD/λ_(cc)+31.73  (19)

is satisfied,

and in each of the four cores, MFD/λ_(cc) and the center-to-centerinterval Λ_(a) between the cores having the adjacent relationshipsatisfy any one of the following Formula (20) to Formula (24):

6.5≤MFD/λ_(cc)≤7.5≤0.392Λ_(a)−4.88  (20);

6.5≤MFD/λ_(cc)≤8.0≤0.392Λ_(a)−4.88  (21);

6.5≤MFD/λ_(cc)≤8.5≤0.392Λ_(a)−4.88  (22);

6.5≤MFD/λ_(cc)≤9.0≤0.392Λ_(a)−4.88  (23); and

6.5≤MFD/λ_(cc)≤9.5≤0.392Λ_(a)−4.88  (24).

The MCF having the above-described structure is a four-core fiberarranged in a square and having a standard cladding diameter, and hasoptical characteristics suited for an O band while ensuring sufficienttolerance in mass production. The relationship between the MFD andλ_(cc) (MFD/λ_(cc)) satisfies the above Formulas (12) and (13), and thusthe leakage loss to the coating of the outermost peripheral core at thewavelength of 1360 nm can be suppressed to 0.01 dB/km or less. Inaddition, in a case where the MCF satisfies the above fifth condition,the tolerance of MFD/λ_(cc) can also be ensured, and the total amount ofthe counter propagation XT to a predetermined core for the fiber lengthof 10 km at the wavelength of 1360 nm or less can be suppressed to −20dB or less with a high yield at the time of fiber mass production.Furthermore, in a case where the MCF satisfies the above sixthcondition, the tolerance of MFD/λ_(cc) can also be ensured, and thetotal amount of the counter propagation XT to the predetermined core forthe fiber length of 10 km at the wavelength of 1360 nm or less can besuppressed to −40 dB or less with a high yield at the time of fiber massproduction. By allowing degradation of the optical characteristics on aC band (1530 nm or more and 1565 nm or less) and an L band (1565 nm ormore and 1625 nm or less), which are long wavelength bands, it becomespossible to realize a wide tolerance in the MCF having opticalcharacteristics suited for the O band. Tolerance of MFD/λ_(cc) can alsobe ensured. In addition, the total amount of the counter propagation XTto a predetermined core for a fiber length of 10 km at the wavelength of1360 nm or less can be suppressed to −40 dB or less, while maintaining ahigh yield at the time of fiber mass production.

(3) According to one aspect of the present disclosure, the MCF mayfurther include a coating surrounding the common cladding and comprisedof, for example, a resin. In such a configuration, preferably, a leakageloss from at least any of the four cores to the coating at a wavelengthof 1550 nm or a wavelength of 1625 nm is 0.05 dB/km or more, atransmission loss of at least one of the four cores at the wavelength of1550 nm is 0.25 dB/km or more, or a transmission loss at the wavelengthof 1625 nm is 0.25 dB/km or more. In this case, by allowing degradationof the optical characteristics on the C band (1530 nm or more and 1565nm or less) and the L band (1565 nm or more and 1625 nm or less), whichare long wavelength bands, it becomes possible to realize a widetolerance in the MCF having optical characteristics suited for the Oband.

(4) According to one aspect of the present disclosure, in the MCF,either the above third condition or the above fifth condition issatisfied, and the XT between the cores having the adjacent relationshipat the wavelength of 1550 nm for the fiber length of 10 km is preferably−10 dB or more. Alternatively, in the MCF, either the above fourthcondition or the above sixth condition is satisfied, and the XT betweenthe cores having the adjacent relationship at the wavelength of 1550 nmfor the fiber length of 10 km is preferably −20 dB or more. In thiscase, by allowing degradation of the optical characteristics on the Cband and the L band, which are long wavelength bands, it becomespossible to realize a wide tolerance in the MCF having opticalcharacteristics suited for the O band.

(5) An MCF cable according to the present disclosure preferably includesa plurality of MCFs including the MCF having the above-describedstructure. In addition, according to one aspect of the presentdisclosure, an MCF ribbon, in which a plurality of MCFs including theMCF having the above-described structure are intermittently bonded, maybe incorporated. According to one aspect of the present disclosure, theMCF cable incorporates an MCF ribbon with spirally twisted. According toany aspect, an increase in transmission capacity is enabled. Inaddition, according to one aspect of the present disclosure, the MCFcable preferably includes a multi-core optical fiber having an averagebending radius of 0.03 in or more and 0.14 in or less, or 0.14 in ormore and 0.3 in or less in a fiber longitudinal direction. In this case,the degradation of the optical characteristics associated with anincrease in bending loss can be effectively suppressed.

Heretofore, each aspect listed in the section of [Descriptions ofEmbodiments of the Present Disclosure] is applicable to each of all theremaining aspects or to all combinations of these remaining aspects.

Details of Embodiments of the Present Disclosure

Hereinafter, specific structures of a multi-core optical fiber (MCF) anda multi-core optical fiber cable (MCF cable) according to the presentdisclosure will be described in detail with reference to theaccompanying drawings. Note that the present disclosure is not limitedto these examples, but is indicated by the claims, and is intended toinclude all modifications within the meaning and scope equivalent to theclaims. In addition, in the description of the drawings, the sameelements are denoted by the same reference numerals, and duplicateddescriptions will be omitted.

FIG. 1 is a diagram illustrating various structures of an MCF cable(including an MCF according to the present disclosure) according to thepresent disclosure.

An MCF cable 1A having a structure (A) includes an outer sheath 300including an MCF accommodation space extending in a longitudinaldirection of the MCF cable 1A, and a plurality of MCFs 100 (MCFsaccording to the present disclosure). In the outer sheath 300, twotensile strength lines (tension members) 400A and 400B extending alongthe MCF accommodation space are embedded. The MCFs 100 each includes aglass fiber 200, the outer periphery surface of which is covered with aresin coating. Note that the MCF 100 can constitute an intermittentlybonded MCF ribbon, and in this case, the MCF ribbon is incorporated intothe MCF cable 1A with spirally twisted.

On the other hand, an MCF cable 1B having a structure (B) includes anouter sheath 500 including an MCF accommodation space extending in alongitudinal direction of the MCF cable 1B, a slotted core 600 thatdivides the MCF accommodation space into a plurality of spaces, and aplurality of MCFs 100 (MCFs according to the present disclosure). Theslotted core 600 that divides the MCF accommodation space into theplurality of spaces is accommodated inside the outer sheath 500. Atensile strength line 700 extending in a longitudinal direction of theMCF cable 1B is embedded in the slotted core 600. The plurality of MCFs100 are accommodated in any one of the spaces divided by the slottedcore 600.

FIG. 2 is a diagram illustrating various core arrangements in the MCFaccording to the present disclosure. In particular, a top part of FIG. 2illustrates a cross-sectional view of a four-core MCF 100A (an MCF 100according to the present disclosure) in which four cores are arranged toform a 3-sides equal trapezoid, a middle part of FIG. 2 illustrates across-sectional view of a four-core MCF 100B (an MCF 100 according tothe present disclosure) in which four cores are respectively arranged atsquare lattice points set at positions shifted from a cladding center,and a bottom part of FIG. 2 illustrates a cross-sectional view of afour-core MCF 100C (an MCF 100 according to the present disclosure) inwhich a marker is additionally provided in the core arrangement of themiddle part. Note that each drawing of FIG. 2 illustrates, as anexample, a combination of first cores 100 a that propagate light in apredetermined direction and second cores 100 b that propagate the lightin an opposite direction.

In the MCF 100 according to the present disclosure, preferably, the corearrangement including the four cores does not have rotational symmetrytwice or more with the cladding center used as a symmetry axis. In thiscase, even without a marker, core symmetry is enabled at the time ofsplicing or at the time of MCF rotation alignment. In this situation,the respective centers of the four cores are preferably arranged to beline symmetric with respect to a straight line as a symmetry axis thatpasses through the cladding center. Accordingly, at the time of splicinganother MCF to the MCF, the core alignment is enabled without thepolarity at either end face of the MCF.

The four-core MCF 100A illustrated in the top part of FIG. 2 includes aglass fiber 200A, and a resin coating 130 for covering the glass fiber200A. The glass fiber 200A includes four cores (in this example, thefirst cores 100 a and the second cores 100 b are included), and a commoncladding 120 surrounding the four cores. On a cross-section of thefour-core MCF 100A, the four cores are respectively allocated to fourvertexes of a 3-sides equal trapezoid, in which three sides have anequal length Λ_(nominal) and the length of the remaining one side issufficiently longer than Λ_(nominal) (a pattern 1 of a corearrangement). In this case, four cores are arranged to surround thecladding center (a fiber axis AX1). Note that the center position ofeach the first cores 100 a and the second cores 100 b is disposed within1.0 μm, preferably within 0.5 μm, and more preferably within 0.25 μmfrom the allocated vertex of the 3-sides equal trapezoid. The length ofthe remaining one side of the above 3-sides equal trapezoid ispreferably 1.2 times or more of Λ_(nominal) Accordingly, the rotationalsymmetry twice or more can be sufficiently lost at the time of endsurface observation, while the inter-core XT is suppressed to apredetermined value or less. In addition, d_(coat) of any corepreferably falls within a range of a value of d_(coat,nominal)−1 μm ormore and a value of d_(coat,nominal)+1 μm or less with a predeterminedd_(coat,nominal) used as a basis. In this case, the rotational symmetrytwice or more can be sufficiently lost at the time of end surfaceobservation, while the leakage loss to the coating is suppressed to apredetermined value or less.

Note that, in the example illustrated in the top part of FIG. 2, astructure serving as a marker does not have to be provided other thanthe cores. In a case where the structure serving as the marker isprovided other than the cores, manufacturing performance is degraded inorder to realize the structure (for example, in a case of amanufacturing method for forming a hole in a cladding preform to inserta core preform, it is necessary to additionally form a hole for a markerto insert a marker preform, serving as a marker having a refractiveindex different from that of the cladding, into the hole). The absenceof the structure serving as the marker other than the cores enables animprovement in the manufacturing performance of the MCF, in the exampleillustrated in the top part of FIG. 2.

The four-core MCF 100B illustrated in the middle part of FIG. 2 includesa glass fiber 200B, and a resin coating 130 for covering the glass fiber200B. The glass fiber 200B includes four cores (in this example, thefirst cores 100 a and the second cores 100 b are included), and thecommon cladding 120 surrounding the four cores. On a cross-section ofthe four-core MCF 100B, the four cores each have a predetermined latticepoint interval Λ_(nominal), and are respectively allocated to latticepoints of a square lattice having four lattice point pairs each havingan adjacent relationship. The middle part of FIG. 2 illustrates, as anexample of the core arrangement, an example (a pattern 2 of the corearrangement) in which the center of the square lattice is shifted fromthe cladding center (coincides with a fiber axis AX2). However, thecenter of the square lattice may coincide with the cladding center. Inthis case, d_(coat) of the respective cores are equal to each other, andthus the optical characteristics can be made uniform. The centerpositions of the four cores are each disposed within 1.0 μm, preferablywithin 0.5 μm, and more preferably within 0.25 μm from the allocatedlattice point of the square lattice. Accordingly, in a case where thefour square lattice points are set as the design positions for the corecenter, it becomes possible to suppress a deviation of the corearrangement, while allowing the dimensional tolerance of the corearrangement. In addition, as compared with the core arrangement in thefour-core MCF 100A illustrated in the top part, it can be expected thatthe uniformity of the residual stress and the like in the cross-sectionapplied to the four cores is improved, and the optical characteristicsof the four cores also become uniform. Note that in the example of themiddle part, the four cores are approximately arranged in a squarelattice shape, and the center-to-center interval Λ between the coreshaving an adjacent relationship falls within a range of a value ofΛ_(nominal)−2.0 μm or more and a value of Λ_(nominal)+2.0 μm or less,preferably a range of a value of Λ_(nominal)−1.0 μm or more and a valueof Λ_(nominal)+1.0 μm or less, and more preferably a range of a value ofΛ_(nominal)−0.5 μm or more and a value of Λ_(nominal)+0.5 μm or less.

The four-core MCF 100C illustrated in the bottom part of FIG. 2 includesa glass fiber 200C, and a resin coating 130 for covering the glass fiber200C. The glass fiber 200C includes four cores (in this example, thefirst cores 100 a and the second cores 100 b are included), and thecommon cladding 120 surrounding the four cores. The bottom part of FIG.2 illustrates, as an example of the core arrangement, on a cross-sectionof the four-core MCF 100C, an example in which the center of the squarelattice is shifted from the cladding center (a fiber axis AX3) in a corearrangement constituted of the four cores, in a similar manner to thecore arrangement in the four-core MCF 100B illustrated in the middlepart. The four-core MCF 100B and the four-core MCF 100C are different inthat a marker 610 is provided (in a pattern 3 of the core arrangement).Note that, also in the example in which the marker 610 is provided inthis manner, the center of the square lattice may coincide with thecladding center. In this case, d_(coat) of the respective cores areequal to each other, and thus the optical characteristics can be madeuniform. The refractive index of the marker 610 is preferably differentfrom the refractive index of the common cladding 120.

FIG. 3 is a diagram for describing main terms (adjacent relationship,cross-sectional structure around cores, parallel propagation andparallel propagation XT (crosstalk), and counter propagation and counterpropagation XT (crosstalk)) used in the present specification.

(Adjacent Relationship)

In the present specification, regarding an adjacent relationship betweenthe cores, in focusing on one specific core of the four cores arrangedon the cross-section of the MCF, a core having a minimumcenter-to-center interval with respect to such one specific core and acore having difference between a center-to-center interval and theminimum center-to-center interval of 2 μm or less is defined as a corehaving an adjacent relationship with such one specific core. That is, asillustrated in FIG. 3, in a case where a core 111 (110 a) is set as aspecific core, a core 112 (110 b) and a core 113 (110 b) are the coreseach having an adjacent relationship with the core 111. Note that thecores are arranged to constitute the square lattice in both the pattern2 and the pattern 3 of FIG. 2. Therefore, the adjacent relationship isnot established between the core 112 (110 b) and the core 113 (110 b) asillustrated in FIG. 3. However, a core 114 (110 a) has an adjacentrelationship with both the core 112 (110 b) and the core 113 (110 b).

(Cross-Sectional Structure Around Cores)

In the four cores having the core arrangements of the patterns 1 to 3illustrated in FIG. 2, according to the present disclosure, in thecross-sectional structure around each core (the first core 110 a or thesecond core 110 b), the common cladding 120 surrounds the outerperiphery of the first core 110 a or the second core 110 b. The commoncladding 120 may be provided to be in direct contact with the first core110 a or the second core 110 b. However, an optical cladding 121 may beprovided between the common cladding 120 and the first core 110 a or thesecond core 110 b. In addition, a trench layer 122 having a smallrelative refractive index difference Δ3 may be provided between theoptical cladding 121 and the common cladding 120. Note that the opticalcladding 121 is prepared for each core, and has a relative refractiveindex difference Δ2 of −0.1% or more and 0.1% or less with respect tothe refractive index of the common cladding 120. Further, in a casewhere a trench layer 122 is provided, the trench layer 122 preferablyhas a relative refractive index difference Δ3 of −0.4% or more and lessthan 0% with respect to the refractive index of the common cladding.

(Parallel Propagation and Parallel Propagation XT)

In the example illustrated in FIG. 3, three cores (the first cores 110 aeach propagating light in an identical direction) in which adjacentrelationships are established are illustrated. That is, the adjacentrelationship is established between the left core and the center core,and the adjacent relationship is established between the center core andthe right core. That is, a state in which the cores each having theadjacent relationship propagate light in the identical direction isreferred to as “parallel propagation”. In this case, a generalinter-core XT (parallel propagation XT) is generated between theadjacent cores (between the cores having an adjacent relationship) thatpropagate light in the identical direction.

(Counter Propagation and Counter Propagation XT)

On the other hand, in counter propagation, light is propagated indirections different from each other between two cores in which theadjacent relationship is established. That is, in the example of FIG. 3,the adjacent relationship is established between the left core and thecenter core. However, the left core functions as the first core 110 a,and the center core functions as the second core 110 b that propagateslight in a direction different from that of the first core 110 a. Thegeneral XT generated between the left core and the center core hardlyaffects the communication quality. In a similar manner, the right corehaving the adjacent relationship with the center core functions as thefirst core 110 a, and the general XT generated between the right coreand the center core hardly affects the communication quality. In thismanner, a state in which the cores having the adjacent relationshippropagate light in different directions from each other is referred toas “counter propagation”. However, between the left core and the rightcore (both of which function as the first cores 110 a), the XT affectsthe communication quality via the center core (which functions as thesecond core 110 b). In this manner, the inter-core XT that propagatesthe light in the identical direction via the core that establishes theadjacent relationship and that propagates the light in the oppositedirection is referred to as “counter propagation XT”.

Note that in the following description, a description will be given withreference to examples of “parallel propagation” and “counterpropagation” illustrated in FIG. 3. However, in a case where XT_(co)(L1)represents an XT (parallel propagation XT: XT_(co)) between the coresbetween which the adjacent relationship is established (hereinafter,referred to as an “adjacent core”) at a fiber length L1, and the XT isrepresented in decibel value, the XT can be expressed in the followingFormula (25):

$\begin{matrix}{{{{XT}_{co}\left( {L\; 2} \right)} = {{{XT}_{co}\left( {L\; 1} \right)} + {10\;\log_{10}\frac{L\; 2}{L\; 1}}}},} & (25)\end{matrix}$

and is increased by 10 dB at a distance of 10 times.

In a case where the XT is represented in decibel value, for example, inthe example of the counter propagation illustrated in FIG. 3, the XT(the counter propagation XT: XT_(counter)) from the right core to theleft core via the center core can be expressed in the following Formula(26):

XT _(counter)=2XT _(co)−10 log₁₀2  (26)

using the parallel propagation XT: XT_(co) between the left core and thecenter core and between the center core and the right core.

In a case where XT_(counter)(L1) represents a counter propagation XT atthe fiber length L1, and XT is expressed in decibel value, the counterpropagation XT at a fiber length L2 can be expressed in the followingFormula (27):

$\begin{matrix}{{{{XT}_{counter}\left( {L\; 2} \right)} = {{{XT}_{counter}\left( {L\; 1} \right)} + {20\;\log_{10}\frac{L\; 2}{L\; 1}}}},} & (27)\end{matrix}$

and is increased by 20 dB at a distance of 10 times.

A total XT_(co,tot) of XT_(co) from an adjacent core to a predeterminedcore is calculated in the following Formula (28):

X _(co,tot) =XT _(co)+10 log₁₀ N  (28),

where N represents the number of adjacent cores to the predeterminedcore.

The total XT_(counter,tot) of XT_(counter) from a specific core havingan adjacent relationship with an adjacent core of the predetermined core(but, having no adjacent relationship with the predetermined core) tothe predetermined core seems to be calculated by the following Formula(29):

XT _(counter,tot) =XT _(counter)+10 log₁₀ M=2XT _(co)−10 log₁₀2+10 log₁₀M  (29),

where M represents the number of the specific cores to the predeterminedcore.

However, the fact is different, and the inventor has discovered that ina case where Kn represents the number of adjacent cores (including thepredetermined core) of an adjacent core n of the predetermined core, thetotal XT_(counter,tot) satisfies the following Formula (30):

$\begin{matrix}{{XT}_{{counter},{tot}} = {{{XT}_{counter} + {10\;\log_{10}{\sum\limits_{n = 1}^{N}\left( {K_{n} - 1} \right)}}} = {{2{XT}_{co}} - {10\;\log_{10}2} + {10\;\log_{10}{\sum\limits_{n = 1}^{N}{\left( {K_{n} - 1} \right).}}}}}} & (30)\end{matrix}$

Thus, in the four-core MCF having a core arrangement in which the fourcores are arranged on a square lattice (hereinafter, referred to as a“square core arrangement”), XT_(counter,tot) to any core is expressed inthe following Formula (31):

XT _(counter,tot) =XT _(counter)+10 log₁₀2=2XT _(co)  (31).

Therefore, in the four-core fiber in which there are only three corepairs each having an adjacent relationship (such as 1×4 core arrangementin which four cores are arranged in one line), XT_(counter,tot) to anycore having two adjacent cores can be expressed in the following Formula(32):

XT _(counter,tot) =XT _(counter)+10 log₁₀1=2XT _(co)−10 log₁₀2  (32).

As described above, in order to set XT_(counter,tot) [dB] after thepropagation for 10 km in the four-core MCF having the square corearrangement to −20 dB or less, the parallel propagation XT (XT_(co))between the adjacent cores in terms of the fiber length L [km] ispreferably expressed in the following Formula (33):

$\begin{matrix}{{{XT}_{co}(L)} \leq {{- 10.0} + {10\;\log_{10}{\frac{L}{10}.}}}} & (33)\end{matrix}$

The sum of the parallel propagation XT from two adjacent cores to anycore is expressed in the following Formula (34):

$\begin{matrix}{{{XT}_{{co},{tot}}(L)} \leq {{- 7.0} + {10\;\log_{10}{\frac{L}{10}.}}}} & (34)\end{matrix}$

In order to set XT_(counter,tot) [dB] after the propagation for 10 km inthe four-core MCF having the square core arrangement to −40 dB or less,the parallel propagation XT (XT_(co)) between the adjacent cores interms of the fiber length L [km] is preferably expressed in thefollowing Formula (35):

$\begin{matrix}{{{XT}_{co}(L)} \leq {{- 20.0} + {10\;\log_{10}{\frac{L}{10}.}}}} & (35)\end{matrix}$

The sum of the parallel propagation XT from two adjacent cores to anycore is preferably expressed in the following Formula (36):

$\begin{matrix}{{{XT}_{{co},{tot}}(L)} \leq {{- 17.0} + {10\;\log_{10}{\frac{L}{10}.}}}} & (36)\end{matrix}$

In order to set XT_(counter,tot) [dB] after the propagation for 10 km to−20 dB or less in the four-core MCF in which there are only three corepairs each having an adjacent relationship (such as 1×4 core arrangementin which four cores are arranged in one line), the parallel propagationXT (XT_(co)) between adjacent cores in terms of the fiber length L [km]is preferably expressed in the following Formula (37):

$\begin{matrix}{{{XT}_{co}(L)} \leq {{- 8.5} + {10\;\log_{10}{\frac{L}{10}.}}}} & (37)\end{matrix}$

The sum of the parallel propagation XT from such adjacent cores to anycore having two adjacent cores is expressed in the following Formula(38):

$\begin{matrix}{{{XT}_{{co},{tot}}(L)} \leq {{- 5.5} + {10\;\log_{10}{\frac{L}{10}.}}}} & (38)\end{matrix}$

In order to set XT_(counter,tot) [dB] after the propagation for 10 km inthe four-core MCF having the square core arrangement to −40 dB or less,the parallel propagation XT (XT_(co)) between the adjacent cores interms of the fiber length L [km] is preferably expressed in thefollowing Formula (39):

$\begin{matrix}{{{XT}_{co}(L)} \leq {{- 18.5} + {10\;\log_{10}{\frac{L}{10}.}}}} & (39)\end{matrix}$

The sum of the parallel propagation XT from the adjacent cores to anycore having two adjacent cores is preferably expressed in the followingFormula (40):

$\begin{matrix}{{{XT}_{{co},{tot}}(L)} \leq {{- 15.5} + {10\;\log_{10}{\frac{L}{10}.}}}} & (40)\end{matrix}$

Next, a profile structure applicable to the MCFs according to thepresent disclosure will be described. FIG. 4 is a diagram illustrating arefractive index profile around each core applicable to the MCFsaccording to the present disclosure. Note that unless otherwisespecified, a “relative refractive index difference Δ” means a relativerefractive index difference with respect to the refractive index of thecommon cladding (and therefore, is not the relative refractive indexdifference with respect to the refractive index of pure silica glass).

Regarding the core structure in the MCF according to the presentdisclosure, an appropriate structure is selectable for the refractiveindex profile of the core and the optical characteristics associatedwith the profile in accordance with the use application. For example,refractive index profiles of a pattern (A) to a pattern (K) illustratedin FIG. 4 are applicable. Note that in FIG. 4, Δ represents a relativerefractive index difference with the refractive index of the commoncladding used as a basis, r represents a radius vector (radius) fromeach core center, and a local coordinate system in which each corecenter and Δ=0%, is set to an origin O is illustrated. Structures may bethe same or different between the cores.

The pattern (A) illustrated in FIG. 4 is a step type refractive indexprofile, the pattern (B) is a ring type refractive index profile, thepattern (C) is a double step type refractive index profile, the pattern(D) is a graded type refractive index profile, and the pattern (E) is afringe type refractive index profile. These are applicable to the corestructure in the MCF according to the present disclosure. Further, thepattern (F) and the pattern (H) in which a Depressed type refractiveindex profile is provided around the core, the pattern (G), the pattern(I), and the pattern (J) in which a Raised type refractive index profileis provided around the core, and the pattern (E) in which a Matched typerefractive index profile is provided around the core are also applicableto the core structure.

For the refractive index profiles other than the step type refractiveindex profile of the pattern (A), a core radius a and Δ (Δ1) of the coreof a case of being approximated by the step type by using anequivalent-step-index (ESI) approximation are obtainable (theabove-described Non-Patent Document 3).

The above-described Non-Patent Document 3 is easily applicable to a casewhere the boundary between the core and the cladding is clear. However,it is difficult to apply the above-described Non-Patent Document 3 to acase where the boundary between the core and the cladding (the commoncladding 120 or the optical cladding 121) is unclear as the fringe typerefractive index profile of the pattern (E). For example, in a casewhere the method of the above-described Non-Patent Document 3 is appliedwithout change with b in the pattern (E) regarded as the radius of thecore, the ESI approximation does not work well. In such a case, it ispreferable to apply the above-described Non-Patent Document 3 with rthat takes 2/5Δ of Δ at r, in which a slope (∂Δ/∂r) of the refractiveindex profile takes a negative value having a largest absolute value,and which is regarded as the core radius a. In this situation, regardingthe refractive index of the cladding (the common cladding 120 or theoptical cladding 121), by using r that is a value obtained from a simpleaverage of Δ in a range from a to b expressed in the following Formula(41):

$\begin{matrix}{{\Delta\; 2} \approx {\int_{a}^{b}{\Delta\;{dr}}}} & (41)\end{matrix}$

or a weighted average with r represented in the following Formula (42):

$\begin{matrix}{{{\Delta\; 2} \approx {\int_{a}^{b}{\Delta\;{{rdr}/{\int_{a}^{b}{rdr}}}}}},} & (42)\end{matrix}$

a and Δ1 (a maximum relative refractive index difference between thefirst core 110 a and the second core 110 b) can be obtained by thecalculation based on the above Non-Patent Document 3. Δ2 (a relativerefractive index difference of the optical cladding 121) is preferably−0.10% or more and 0.10% or less. This is because the manufacturingperformance is largely improved.

The trench layer 122 having a refractive index lower than those of theoptical cladding 121 and the common cladding 120 may be provided aroundthe optical cladding 121 (the pattern (K) in FIG. 4). However, in a casewhere a relative refractive index difference Δ3 of the trench layer 122with the refractive index of the common cladding 120 used as a basis is−0.5% or less, the manufacturing performance is largely degraded.Therefore, Δ3≥−0.4% is preferable, Δ3≥−0.3% is more preferable, andΔ3≥−0.2% is further preferable. Note that from the viewpoint of themanufacturing performance, the absence of the trench layer is morepreferable.

Regarding the material of the core and the cladding (the opticalcladding 121 or the common cladding 120), glass containing silica glassas a main component is preferable, because a low transmission loss andhigh mechanical reliability are achievable. By adding Ge to the core, arefractive index difference generated between the core and the claddingis preferable. Alternatively, by adding F to the cladding, a refractiveindex difference generated between the core and the cladding ispreferable. By adding a minute amount of F to the core and the opticalcladding, a Depressed type profile is achievable with good manufacturingperformance, and is preferable. Cl may be added to the core or thecladding. This enables suppression of an OH group and suppression of anabsorption loss caused by the OH group. A minute amount of P may becontained in the core or the cladding. This enables an enhancement inmanufacturing performance in a part of a glass synthesis process.

The MCF according to the present disclosure having the cross-sectionalstructure illustrated in FIG. 2 includes the resin coating 130. Thediameter of the resin coating 130 preferably falls within a range of 235μm or more and 265 μm or less with 250 μm used as a basis. Accordingly,the MCF according to the present disclosure formed into a cable isenabled without making a significant change to existing cablingfacilities or the like.

In a typical general-purpose SMF, the nominal value CD_(nominal) of thecladding diameter is 125 μm, and the nominal value of the coatingdiameter is approximately 245 μm or more and 250 μm or less. However,the coating diameter is preferably 160 gm or more and 230 μm or less,because the number of accommodated optical fibers per unit cross-sectionin a cable can be increased.

The MCF according to the present disclosure is a four-core MCF asdescribed above. The number of the cores is an even number, and is apower of 2. Therefore, it is desirable to use as the number of spatialchannels for communication.

Further, in the MCF according to the present disclosure, the arrangementof the centers of the four cores (substantially the core arrangement) isline symmetric with respect to a straight line as a symmetry axis thatpasses through the cladding center. However, preferably, there is norotational symmetry more than once. Accordingly, even without a marker,core symmetry is enabled at the time of fiber splicing or at the timeMCF rotation alignment. In this situation, the centers of theabove-described four cores are preferably arranged to be line symmetricwith respect to a straight line as a symmetry axis that passes throughthe cladding center. Accordingly, at the time of splicing the MCF toanother MCF, the core alignment is enabled without the polarity ateither end face of the MCF.

For example, in the example illustrated in the top part of FIG. 2, alsoin the MCF, on the cross-section, the cores are respectively allocatedat four vertexes of the 3-sides equal trapezoid in which three sideseach have an equal length Λ_(nominal) and the remaining one side has alength sufficiently longer than Λ_(nominal). In this situation,preferably, the center position of each core is disposed within 1.0 μm,preferably within 0.5 μm, and more preferably within 0.25 μm from thecorresponding vertex of the 3-sides equal trapezoid. The length of theabove-described remaining one side of the 3-sides equal trapezoid ispreferably 1.2 times or more of Λ_(nominal). Accordingly, the rotationalsymmetry twice or more can be sufficiently lost at the time of endsurface observation, while the inter-core XT is suppressed to apredetermined value or less.

In addition, preferably, d_(coat) of any core falls within a range of avalue of d_(coat,nominal)−1 μm or more and a value of d_(coat,nominal)+1μm or less with a predetermined nominal value d_(coat,nominal) used as abasis. Accordingly, the rotational symmetry twice or more can besufficiently lost at the time of end surface observation, while theleakage loss to the coating is suppressed to a predetermined value orless.

The MCF according to the present disclosure preferably has no structureserving as a marker other than the cores. This is because the provisionof the structure serving as the marker other than the cores degrades themanufacturing performance in order to realize the structure. Forexample, in the case of the manufacturing method for forming the hole inthe cladding preform to insert the core preform, it is necessary toadditionally form the hole for the marker and insert the marker preform(the preform serving as the marker) having a refractive index differentfrom that of the cladding, into the hole. Conversely, the absence of thestructure serving as the marker other than the cores enables animprovement in the manufacturing performance of the MCF according to thepresent disclosure.

In addition, as illustrated in the MCF in the middle part of FIG. 2according to the present disclosure, the core arrangement in which thereare four core pairs each having an adjacent relationship in the fourcores, that is, a square lattice arrangement may be employed. Note thatin this case, the center position of the square lattice is shifted fromthe cladding center in order to sufficiently lose the rotationalsymmetry twice or more about the cladding center. The centers of thefour cores are respectively arranged within 1.0 μm, preferably within0.5 μm, and more preferably within 0.25 μm from the four lattice pointsof the square lattice each having a predetermined lattice point intervalΛ_(nominal). Accordingly, in a case where the four lattice points of thesquare lattice are set as the design positions of the core center, itbecomes possible to suppress shifting of the core arrangement, whileallowing the dimensional tolerance of the core arrangement. In addition,as compared with the core arrangement of the 3-sides equal trapezoidillustrated in the top part of FIG. 2, the four-core arrangement in asquare lattice shape is desirable, because the residual stress and thelike in the cross-section applied to the four cores become uniform, andthe optical characteristics of the four cores also become uniform. Notethat, in the above-described configuration, it can be rephrased thatfour cores are approximately arranged in a square lattice shape, and thecenter-to-center interval Λ between the adjacent cores falls within arange of a value of Λ_(nominal) 2.0 μm or more and a value ofΛ_(nominal)+2.0 μm or less, preferably a range of a value ofΛ_(nominal)−1.0 μm or more and a value of Λ_(nominal)+1.0 μm or less,and more preferably a range of a value of Λ_(nominal)−0.5 μm or more anda value of Λ_(nominal)+0.5 μm or less.

Note that in the MCF according to the present disclosure, aconfiguration in which the marker is arranged like the exampleillustrated in the bottom part of FIG. 2 is not excluded. In summary ofthe above conditions, there are three to four core pairs each having anadjacent core relationship among the four cores, the center positions ofthe four cores are arranged to be line symmetric with respect to astraight line as a symmetry axis that passes through the cladding centerand that does not pass through the center of any core. Further, in acase where there are only three core pairs each having an adjacent corerelationship, preferably, the arrangement of the core center with thecladding center as the symmetry axis does not have the rotationalsymmetry twice or more.

In addition, the MCF cable according to the present disclosurepreferably includes a plurality of MCFs including the MCF having theabove-described structure. As an example, the MCF cable may incorporatean MCF ribbon in which a plurality of MCFs including the MCF having theabove-described structure are intermittently bonded. In the MCF cable,the MCF ribbon is incorporated with spirally twisted. Any of theconfigurations enables an increase in transmission capacity.Furthermore, the MCF cable preferably includes a multi-core opticalfiber having an average bending radius of 0.03 in or more and 0.14 in orless, or 0.14 in or more and 0.3 in or less in a fiber longitudinaldirection. In this case, the degradation of the optical characteristicsassociated with an increase in bending loss can be effectivelysuppressed.

Each core in the MCF according to the present disclosure preferablyincludes an MFD that falls within a range of a value of the MFDreference value−0.4 μm or more and a value of the MFD referencevalue+0.4 μm or less, with a value of 8.6 μm or more and 9.2 μm or lessat a wavelength of 1310 nm used as an MFD reference value. In this case,among the general-purpose SMFs regulated in ITU-T G652, in particular,as compared with a splice loss between the general-purpose SMFs of atype in which the nominal value of the MFD MFD_(nominal) is small(MFD_(nominal)≈8.6 μm) and a bending loss is suppressed, a splice losscaused by an axis deviation between the MCFs according to the presentdisclosure (in a case where a predetermined axis deviation is given) canbe made equal or less.

Each core in the MCF according to the present disclosure preferablyincludes an MFD that falls within a range of 8.2 μm or more and 9.0 μmor less with 8.6 μm used as a basis at the wavelength of 1310 nm.Accordingly, among the general-purpose SMFs regulated in ITU-T G652,regarding the splice between a general-purpose SMF of a type in whichthe nominal value of the MFD is small and the bending loss is suppressedand the MCF according to the present disclosure, a splice loss caused bya core central axis deviation (an axis deviation) (in a case where apredetermined axis deviation is given) can be made equal.

The MCF according to the present disclosure preferably has azero-dispersion wavelength of 1300 nm or more and 1324 nm or less.Accordingly, a distortion of the signal waveform after transmission onan O-band can be suppressed to an extent same as that of thegeneral-purpose SMF.

The MCF according to the present disclosure preferably has azero-dispersion wavelength that falls within a range of a value of thewavelength reference value −12 nm or more and a value of the wavelengthreference value+12 nm or less, with a predetermined value uses as awavelength reference value of 1312 nm or more and 1340 nm or less.Accordingly, a distortion of the signal waveform after transmission onthe O-band can be suppressed more than that of the general-purpose SMF(see the above-described Non-Patent Document 4).

In the MCF according to the present disclosure, on the used wavelengthband, the total sum of the XT from an adjacent core to any core ispreferably −20 dB or less, even after the propagation for 10 km. The XTfrom the core other than the adjacent cores is sufficiently low and canbe ignored. Therefore, a sufficient signal-to-noise ratio is achievableeven in a case where a coherent wave is detected. In addition, in theMCF according to the present disclosure, on the used wavelength band,the total sum of the XT from an adjacent core to any core is preferably−40 dB or less, even after the propagation for 10 km. The XT from thecore other than the adjacent cores is sufficiently low and can beignored. Therefore, a sufficient signal-to-noise ratio is achievableeven in a case where an intensity modulation wave is directly detected.In the MCF according to the present disclosure, on the used wavelengthband, the parallel propagation XT is preferably −10.0 dB or less, evenafter the propagation for 10 km. Accordingly, the counter propagation XTcan be reduced to −20 dB or less even after the propagation for 10 km.Furthermore, in the MCF according to the present disclosure, on the usedwavelength band, the parallel propagation XT is preferably −20.0 dB orless, even after the XT parallel propagation for 10 km. Accordingly, thecounter propagation XT can be reduced to −40 dB or less, even after thepropagation for 10 km.

In the following description, a description will be given with regard tostudied results about an MCF including cores having the refractive indexprofiles of the pattern (E), the pattern (H), and the pattern (J) ofFIG. 4, and having a of 3 μm or more and 5 μm or less, Δ1−Δ2 of 0.3% ormore and 0.6% or less, Δ2 of −0.1% or more and 0.1% or less, and b/a of2 or more and 5 or less.

The core structure having a predetermined zero-dispersion wavelength andthe MFD can be designed by those skilled in the art by calculating anelectric field distribution in a fundamental mode and a wavelengthdependency of an effective refractive index using a finite elementmethod or the like. For example, in ranges of 3 μm≤a≤5 μm and0.3%≤(Δ1−Δ2)≤0.6%, the relationship between a and (Δ1−Δ2) to be azero-dispersion wavelength λ₀ [μm], is expressed in the followingFormula (43):

a≈0.0667(λ₀−1343.1)Δ1−Δ2)²+0.0900(λ₀−1354.6)(Δ1−Δ2)−0.0517(λ₀−1411.2)  (43).

Therefore, in order for the zero-dispersion wavelength λ₀ [μm] to fallwithin the range of a value of λ_(0nominal)−12 nm or more and a value ofλ_(0nominal)+12 nm or less, the relationship between a and (Δ1−Δ2)preferably satisfies both the following Formulas (44) and (45):

a≤0.0667(λ_(nominal)−12−1343.1)(Δ1−Δ2)²+0.0900(λ_(nominal)−12−1354.6)(Δ1−Δ2)−0.0517(λ_(nominal)−12−1411.2)  (44); and

a≥0.0667(λ_(nominal)+12−1343.1)(Δ1−Δ2)²+0.0900(λ_(nominal)+12−1354.6)(Δ1−Δ2)−0.0517(λ_(nominal)+12−1411.2)  (45).

In addition, the relationship between a and (Δ1−Δ2) with respect to MFD[μm] at the wavelength of 1310 nm, in the ranges of 3 μm≤a≤5 μm and0.3%≤(Δ1−Δ2)≤0.6%, is expressed in the following Formula (46):

(Δ1−Δ2)=(−0.0148MFD+0.213)[a−0.619MFD+2.01]²−0.0771MFD+1.033   (46).

Therefore, in order for the MFD [pm] to fall within a range of a valueof MFD_(nominal)−0.4 μm or more and a value of MFD_(nominal)+0.4 μm orless, the relationship between a and (Δ1−Δ2) preferably satisfies thefollowing Formulas (47) and (48):

(Δ1−Δ2)≤[−0.0148(MFD_(nominal)+0.4)+0.213][a−0.619(MFD_(nominal)+0.4)+2.01]²−0.0771(MFD_(nominal)+0.4)+1.033  (47); and

(Δ1−Δ2)≥[−0.0148(MFD_(nominal)−0.4)+0.213][a−0.619)(MFD_(nominal)−0.4)+2.01]²−0.0771(MFD_(nominal)−0.4)+1.033  (48).

It is sufficient to set b/a and Δ2 so that λ_(cc) is 1260 nm or less or1360 nm or less, and the zero-dispersion slope is 0.092 ps/(nm²·km). Forthis purpose, Δ2 preferably falls within a range of −0.1% or more and0.0% or less, and b/a preferably falls within a range of 2 or more and 4or less.

Next, a preferable center-to-center interval Λ between adjacent coreswill be described. FIG. 4 is a graph illustrating a relationship betweenthe center-to-center interval Λ between the adjacent cores andMFD/λ_(cc) of a case where the counter propagation XT at the wavelengthof 1360 nm after the propagation for 10 km (corresponding to the fiberlength of 10 km) is −20 dB (=−20 dB/10 km), in the four-core MCF havinga square core arrangement. Here, an average value R of the fiber bendingradii is 0.14 m. As long as R is 0.14 in or less, a lower XT isachievable. Note that λ_(cc) denotes a cable cutoff wavelength that hasbeen measured with a configuration (a fiber that is not formed into acable) of FIG. 12 of ITU-T G.650.1(March/2018).

In order to set the counter propagation XT after the propagation for 10km at the wavelength of 1360 nm to −20 dB (=−20 dB/10 km) or less, thecenter-to-center interval Λ between the adjacent cores and MFD/λ_(cc)satisfy at least one of the following Formula (49) and Formula (50) (aregion above a lower dotted line illustrated in FIG. 5):

Λ≥2.26MFD/λ_(cc)+12.0  (49); and

MFD/λ_(cc)≤0.443Λ−5.33  (50),

and preferably satisfy at least one of the following Formula (51) andFormula (52) (a region above an upper dotted line illustrated in FIG.5):

Λ>2.26MFD/λ_(cc)+14.5  (51); and

MFD/λ_(cc)≤0.443Λ−6.42  (52).

FIG. 6 is a graph illustrating a relationship between thecenter-to-center interval Λ between the adjacent cores and MFD/λ_(cc) ofa case where the counter propagation XT after the propagation for 10 km(corresponding to the fiber length of 10 km) of the four-core MCF is −20dB and a case where parallel propagation XT after the propagation for 10km (corresponding to the fiber length of 10 km) of the four-core MCF is−20 dB, at both the wavelength of 1550 nm and the wavelength of 1360 nm.Note that in FIG. 6, the above-described relationships are illustratedsuch that a symbol “●” represents the parallel propagation XT at thewavelength of 1550 nm, a symbol “0 (indicated by hatching in FIG. 6)”represents the parallel propagation XT at the wavelength of 1360 nm, asymbol “□” represents the counter propagation XT at the wavelength of1550 nm, and a symbol “▪ (indicated by hatching in FIG. 6)” representsthe counter propagation XT at the wavelength of 1360 nm.

Although no dotted line is illustrated in FIG. 6, in order to set theparallel propagation XT after the propagation for 10 km at thewavelength of 1360 nm to −20 dB or less in a similar manner to theabove-described case of FIG. 5, the center-to-center interval Λ betweenthe adjacent cores and MFD/λ_(cc) satisfy at least one of the followingFormula (53) and Formula (54):

Λ≥2.64MFD/λ_(cc)+12.6  (53); and

MFD/λ_(cc)≤0.379Λ−4.76  (54),

and preferably satisfy at least one of the following Formula (55) andFormula (56):

Λ≥2.64MFD/λ_(cc)+15.0  (55); and

MFD/λ_(cc)≤0.379Λ−5.68  (56).

In order to set the counter propagation XT after the propagation for 10km at the wavelength of 1550 nm to −20 dB or less, the center-to-centerinterval Λ between the adjacent cores and MFD/λ_(cc) satisfy at leastone of the following Formula (57) and Formula (58):

Λ≥3.13MFD/λ_(cc)+10.7  (57); and

MFD/λ_(cc)≤0.320Λ−3.42  (58),

and preferably satisfy at least one of the following Formula (59) andFormula (60):

Λ3.13MFD/λ_(cc)+13.4  (59); and

MFD/λ_(cc)≤0.320Λ−4.29  (60).

In order to set the parallel propagation XT after the propagation for 10km at the wavelength of 1550 nm to −20 dB or less, the center-to-centerinterval Λ between the adjacent cores and MFD/λ_(cc) satisfy at leastone of the following Formula (61) and Formula (62):

Λ≥3.66MFD/λ_(cc)+10.8  (61); and

MFD/λ_(cc)≤0.273Λ−2.95  (62),

and preferably satisfy at least one of the following Formula (63) andFormula (64):

Λ≥3.66MFD/λ_(cc)+13.7  (63); and

MFD/λ_(cc)≤0.273Λ−3.74  (64).

FIG. 7 is a graph illustrating a relationship between thecenter-to-center interval Λ between the adjacent cores and MFD/λ_(cc) ofa case where the counter propagation XT after the propagation for 10 km(corresponding to the fiber length of 10 km) of the four-core MCF is −40dB and a case where the parallel propagation XT after the propagationfor 10 km (corresponding to the fiber length of 10 km) of the four-coreMCF is −40 dB, at both the wavelength of 1550 nm and the wavelength of1360 nm. Note that in FIG. 7, the above-described relationships areillustrated such that a symbol “∘” represents the parallel propagationXT at the wavelength of 1550 nm, a symbol “● (indicated by hatching inFIG. 7)” represents the parallel propagation XT at the wavelength of1360 nm, a symbol “□” represents the counter propagation XT at thewavelength of 1550 nm, and a symbol “▪ (indicated by hatching in FIG.7)” represents the counter propagation XT at the wavelength of 1360 nm.

Although no dotted line is illustrated in FIG. 7, either, in order toset the counter propagation XT after the propagation for 10 km at thewavelength of 1360 nm to −40 dB or less in a similar manner to theabove-described case of FIG. 5, the center-to-center interval Λ betweenthe adjacent cores and MFD/λ_(cc) satisfy at least one of the followingFormula (65) and Formula (66):

Λ≥2.55MFD/λ_(cc)+12.4  (65); and

MFD/λ_(cc)≤0.392Λ−4.88  (66).

and preferably satisfy at least one of the following Formula (67) andFormula (68):

Λ≥2.55MFD/λ_(cc)+14.9  (67); and

MFD/λ_(cc)≤0.392Λ−5.83  (68).

In order to set the parallel propagation XT after the propagation for 10km at the wavelength of 1360 nm to −40 dB or less, the center-to-centerinterval Λ between the adjacent cores and MFD/λ_(cc) satisfy at leastone of the following Formula (69) and Formula (70):

Λ≥3.22MFD/λ_(cc)+13.4  (69); and

MFD/λ_(cc)≤0.310Λ−4.16  (70),

and preferably satisfy at least one of the following Formula (71) andFormula (72):

Λ≥3.22MFD/λ_(cc)+15.7  (71); and

MFD/λ_(cc)≤0.310Λ−4.88  (72).

In order to set the counter propagation XT after the propagation for 10km at the wavelength of 1550 nm to −40 dB or less, the center-to-centerinterval Λ between the adjacent cores and MFD/λ_(cc) satisfy at leastone of the following Formula (73) and Formula (74):

Λ≥3.54MFD/λ_(cc)+10.8  (73); and

MFD/λ_(cc)≤0.283Λ−3.05  (74),

and preferably satisfy at least one of the following Formula (75) andFormula (76):

Λ≥3.54MFD/λ_(cc)+13.6  (75); and

MFD/λ_(cc)≤0.283Λ−3.85  (76).

In order to set the parallel propagation XT after the propagation for 10km at the wavelength of 1550 nm to −40 dB or less, the center-to-centerinterval Λ between the adjacent cores and MFD/λ_(cc) satisfy at leastone of the following Formula (77) and Formula (78):

Λ≥4.47MFD/λ_(cc)+11.0  (77); and

MFD/λ_(cc)≤0.223Λ−2.46  (78),

and preferably satisfy at least one of the following Formula (79) andFormula (80):

Λ≥4.47MFD/λ_(cc)+14.1  (79); and

MFD/λ_(cc)≤0.223Λ−3.16  (80).

In order to allow the position of each core to vary from the designcenter, Λ preferably takes a margin of 1 μm from the range in each ofthe above Formulas. Therefore, in order to set the counter propagationXT after the propagation for 10 km at the wavelength of 1360 nm to −20dB or less, the nominal value Λ_(nominal) of A preferably satisfies atleast the following Formula (81):

Λ_(nominal)≥2.26MFD/λ_(cc)+12.0+1.0  (81),

and more preferably satisfies the following Formula (82):

Λ_(nominal)≥2.26MFD/λ_(cc)+14.5+1.0  (82).

In order to set the parallel propagation XT after the propagation for 10km at the wavelength of 1360 nm to −20 dB or less, the nominal valueΛ_(nominal) preferably satisfies at least the following Formula (83):

Λ_(nominal)≥2.64MFD/λ_(cc)+12.6+1.0  (83),

and more preferably satisfies the following Formula (84):

Λ_(nominal)≥2.64MFD/λ_(cc)+15.0+1.0  (84).

In order to set the counter propagation XT after the propagation for 10km at the wavelength of 1550 nm to −20 dB or less, the nominal valueΛ_(nominal) preferably satisfies at least the following Formula (85):

Λ_(nominal)≥3.13MFD/λ_(cc)+10.7+1.0  (85),

and more preferably satisfies the following Formula (86):

Λ_(nominal)≥3.13MFD/λ_(cc)+13.4+1.0  (86).

In order to set the parallel propagation XT after the propagation for 10km at the wavelength of 1550 nm to −20 dB or less, the nominal valueΛ_(nominal) preferably satisfies at least the following Formula (87):

Λ_(nominal)≥3.66MFD/λ_(cc)+10.8+1.0  (87),

and more preferably satisfies the following Formula (88):

Λ_(nominal)≥3.66MFD/λ_(cc)+13.7+1.0  (88).

In order to set the counter propagation XT at the wavelength of 1360 nmto −40 dB or less, the nominal value Λ_(nominal) preferably satisfies atleast the following Formula (89):

Λ_(nominal)≥2.55MFD/λ_(cc)+12.4+1.0  (89),

and more preferably satisfies the following Formula (90):

Λ_(nominal)≥2.55MFD/λ_(cc)+14.9+1.0  (90).

In order to set the parallel propagation XT after the propagation for 10km at the wavelength of 1360 nm to −40 dB or less, the nominal valueΛ_(nominal) preferably satisfies at least the following Formula (91):

Λ_(nominal)≥3.22MFD/λ_(cc)+13.4+1.0  (91),

and more preferably satisfies the following Formula (92):

Λ_(nominal)≥3.22MFD/λ_(cc)+15.7+1.0  (92).

In order to set the counter propagation XT after the propagation for 10km at the wavelength of 1550 nm to −40 dB or less, the nominal valueΛ_(nominal) satisfies at least the following Formula (93):

Λ_(nominal)≥3.54MFD/λ_(cc)+10.8+1.0  (93),

and more preferably satisfies the following Formula (94):

Λ_(nominal)≥3.54MFD/λ_(cc)+13.6+1.0  (94).

In order to set the parallel propagation XT after the propagation for 10km at the wavelength of 1550 nm to −40 dB or less, the nominal valueΛ_(nominal) preferably satisfies at least the following Formula (95):

Λ_(nominal)≥4.47MFD/λ_(cc)+11.0+1.0  (95),

and more preferably satisfies the following Formula (96):

Λ_(nominal)≥4.47MFD/λ_(cc)+14.1+1.0  (96).

Regarding the above Λ_(nominal), Λ is preferably expressed in thefollowing Formula (97):

Λ_(nominal)−0.9≤Λ≤Λ_(nominal)+0.9  (97).

This can be considered as an approximation of a case where the positionof each core independently varies from the design center with Gaussiandistribution of 3σ=0.9 μm being as probability distribution. In thissituation, the probability that Λ does not satisfy any one of the abovepredetermined Formulas (81) to (96) for defining Λ_(nominal) issuppressed to 1% or less. Furthermore, regarding Λ_(nominal), Λpreferably satisfies the following Formula (98):

Λ_(nominal)−0.7≤Λ≤Λ_(nominal)+0.7  (98).

This can be considered as an approximation of a case where the positionof each core independently varies from the design center with Gaussiandistribution of 3σ=0.7 μm being as probability distribution. In thissituation, the probability that Λ does not satisfy any one of the abovepredetermined Formulas (81) to (96) for defining Λ_(nominal) issuppressed to 0.1% or less. Furthermore, regarding Λ_(nominal), Λpreferably satisfies the following Formula (99):

Λ_(nominal)−0.5≤Λ≤Λ_(nominal)+0.5  (99).

This can be considered as an approximation of a case where the positionof each core independently varies from the design center with Gaussiandistribution of 36=0.5 μm being as probability distribution. In thissituation, a probability that Λ does not satisfy any one of the abovepredetermined Formulas (81) to (96) for defining Λ_(nominal) issuppressed to 0.001% or less.

Next, a description will be given with regard to desirable d_(coat) (theshortest distance from the interface between the resin coating and thecladding to the core center). FIG. 8 is a graph illustrating arelationship between d_(coat) and MFD/λ_(cc) of a case where a leakageloss to the coating at the wavelength of 1360 nm is 0.01 dB/km, in thefour-core MCF.

In order to set the leakage loss to the resin coating to 0.01 dB/km atthe wavelength of 1360 nm, d_(coat) and MFD/λ_(cc) satisfy at least oneof the following Formula (100) and Formula (101) (a region above a lowerdotted line illustrated in FIG. 8):

d _(coat)≥2.88MFD/λ_(cc)+5.36  (100); and

MFD/λ_(cc)≤0.347d _(coat)−1.86  (101).

Furthermore, d_(coat) and MFD/λ_(cc) preferably satisfy at least one ofthe following Formula (102) and Formula (103) (a region above the upperdotted line illustrated in FIG. 8):

d _(coat)≥2.88MFD/λ_(cc)+6.95  (102); and

MFD/λ_(cc)≤0.347d _(coat)−2.41  (103).

d_(coat) of the outermost peripheral core (that is, the minimum value ofd_(coat)) is generally referred to as an outer cladding thickness (OCT).However, d_(coat) according to the present disclosure is defined as avalue that can be regulated for each core.

In order to allow the position of each core to vary from the designcenter and to allow the cladding diameter to vary from the designcenter, d_(coat) preferably takes a margin of at least 1 μm from theranges of the above Formulas (100) to (103). Thus, regarding d_(coat),by setting a nominal value of d_(coat) to d_(coat),nominal, at least thefollowing Formula (104):

d _(coat,nominal)≥2.88MFD/λ_(cc)+5.36+1.0  (104)

is satisfied.

Furthermore, the nominal value CD_(nominal) of the cladding diameter ispreferably set to satisfy the following Formula (105):

d _(coat,nominal)≥2.88MFD/λ_(cc)+6.95+1.0  (105).

In this situation, both the following Formulas (106) and (107):

Λ_(nominal)−0.9≤Λ≤Λ_(nominal)+0.9  (106); and

CD _(nominal)−0.9≤CD≤CD _(nominal)+0.9  (107)

are preferably satisfied.

The probability that d_(coat) does not satisfy at least one of Formula(100) and Formula (102) is suppressed to 1% or less. Further, both thefollowing Formulas (108) and (109):

Λ_(nominal)−0.7≤Λ≤Λ_(nominal)+0.7  (108); and

Λ_(nominal)−0.7≤CD≤CD _(nominal)+0.9  (109)

are preferably satisfied.

In this situation, the probability that d_(coat) does not satisfy atleast one of Formula (100) and Formula (102) is suppressed to 0.1% orless.

Further, both the following Formulas (110) and (111):

Λ_(nominal)−0.5≤Λ≤Λ_(nominal)+0.5  (110); and

CD _(nominal)−0.5≤CD≤CD _(nominal)+0.5  (111)

are preferably satisfied.

In this situation, the probability that d_(coat) does not satisfy atleast one of Formula (100) and Formula (102) is suppressed to 0.001% orless.

Next, a minimum allowable CD_(nominal) will be described. FIG. 9 is agraph illustrating a relationship between a CD (an allowable minimumcladding diameter) and MFD/λ_(cc) of a case where a margin of 1 μm isadded to d_(coat), when the leakage loss to the coating at thewavelength of 1360 nm is 0.01 dB/km, and the margin of 1 μm is added toA, when the counter propagation XT at the wavelength of 1360 nm afterthe propagation for 10 km (corresponding to the fiber length of 10 km)is −20 dB (=−20 dB/10 km), in the four-core MCF. Note that in FIG. 9, ina case where x axis indicates MFD/λ_(cc) and y axis indicates CD, anupper dotted line is represented by y=8.95x+37.47 (x=0.1117y−4.186), anda lower dotted line is represented by y=8.95x+31.13 (x=0.1117y−3.478).

In order to set the leakage loss to the coating at the wavelength of1360 nm to 0.01 dB/km or less and to set the counter propagation XTafter the propagation for 10 km to −20 dB or less in consideration ofthe tolerance in the dimensions of the core position and the claddingdiameter, the relationship between CD_(nominal) and MFD/λ_(cc) satisfiesat least one of the following Formula (112) and Formula (113) (a regionabove the lower dotted line in FIG. 9):

CD _(nominal)≥8.95MFD/λ_(cc)+31.13  (112); and

MFD/λ_(cc)≤0.1117CD _(nominal)−3.478  (113),

and preferably further satisfies at least one of the following Formula(114) and Formula (115) (a region above the upper dotted line in FIG.9):

CD _(nominal)>8.95MFD/λ_(cc)+37.47  (114); and

MFD/λ_(cc)≤0.1117CD _(nominal)−4.186  (115).

FIG. 10 is a graph illustrating a relationship between the CD (theallowable minimum cladding diameter) and MFD/λ_(cc) of a case where amargin of 1 μm is added to d_(coat) and the margin of 1 μm is added toA, when the leakage loss to the coating is 0.01 dB/km, under a conditionthat the counter propagation XT after the propagation for 10 km(corresponding to the fiber length of 10 km) of the four-core MCF is −20dB (=−20 dB/10 km) and the parallel propagation XT (an XT at generalpropagation in an identical direction) after the propagation for 10 km(corresponding to the fiber length of 10 km) is −20 dB (=−20 dB/10 km),at both the wavelength of 1550 nm and the wavelength of 1360 nm. Notethat in FIG. 10, the above-described relationships are illustrated suchthat a symbol “∘” represents the parallel propagation XT at thewavelength of 1550 nm, a symbol “● (indicated by hatching in FIG. 10)”represents the parallel propagation XT at the wavelength of 1360 nm, asymbol “□” represents the counter propagation XT at the wavelength of1550 nm, and a symbol “▪ (indicated by hatching in FIG. 10)” representsthe counter propagation XT at the wavelength of 1360 nm.

Although no dotted line is illustrated in FIG. 10, in the four-core MCFhaving the square core arrangement in a similar manner to the case ofFIG. 5 or the like, in order to set the leakage loss to the coating atthe wavelength of 1360 inn to 0.01 dB/km or less and to set the parallelpropagation XT after the propagation for 10 km to −20 dB or less, inconsideration of the tolerance in the dimensions of the core positionand the cladding diameter, the relationship between CD_(nominal) andMFD/λ_(cc) satisfies at least one of the following Formula (116) andFormula (117):

CD _(nominal)≥9.49MFD/λ_(cc)+31.91  (116); and

MFD/λ_(cc)≤0.1054CD _(nominal)−3.363  (117),

and preferably further satisfies at least one of the following Formula(118) and Formula (119):

CD _(nominal)≥9.49MFD/λ_(cc)+38.16  (118); and

MFD/λ_(cc)≤0.1054CD _(nominal)−4.021  (119).

In order to set the leakage loss to the coating at the wavelength of1550 nm to 0.01 dB/km or less and to set the counter propagation XTafter the propagation for 10 km to −20 dB or less, the relationshipbetween CD_(nominal) and MFD/λ_(cc) satisfies at least one of thefollowing Formula (120) and Formula (121):

CD _(nominal)≥12.56MFD/λ_(cc)+24.30  (120); and

MFD/λ_(cc)≤0.07960CD _(nominal)−1.934  (121),

and preferably further satisfies at least one of the following Formula(122) and Formula (123):

CD _(nominal)≥12.56MFD/λ_(cc)+33.78  (122); and

MFD/λ_(cc)≥0.07960CD _(nominal)−2.688  (123).

In order to set the leakage loss to the coating at the wavelength of1550 nm to 0.01 dB/km or less and to set the parallel propagation XTafter the propagation for 10 km to −20 dB or less, the relationshipbetween CD_(nominal) and MFD/λ_(cc) satisfies at least one of thefollowing Formula (124) and Formula (125):

CD _(nominal)≥13.31MFD/λ_(cc)+24.47  (124); and

MFD/λ_(cc)≤0.07511CD _(nominal)−1.838  (125),

and preferably satisfies at least one of the following Formula (126) andFormula (127):

CD _(nominal)≥13.31MFD/λ_(cc)+34.18  (126); and

MFD/λ_(cc)≤0.07511CD _(nominal)−2.567  (127).

In the four-core fiber having the square core arrangement, in order toset the leakage loss to the coating at the wavelength of 1360 nm to 0.01dB/km or less and to set the counter propagation XT after thepropagation for 10 km to −20 dB or less, in consideration of thetolerance in the dimensions of the core position and the claddingdiameter, in a case where CD_(nominal) is 125 μm, 120 μin, 115 μin, 110μin, 105 μm, 100 μm, 95 μm, 90 μm, 85 μm, and 80 μm, MFD/λ_(cc) ispreferably 10.49 or less, 9.93 or less, 9.37 or less, 8.81 or less, 8.25or less, 7.69 or less, 7.14 or less, 6.58 or less, 6.02 or less, or 5.46or less in the order of numerical values of the CD_(nominal) as listedabove, and MFD/λ_(cc) is more preferably 9.78 or less, 9.22 or less,8.66 or less, 8.10 or less, 7.54 or less, and 6.99 or less, 6.43 orless, 5.87 or less, 5.31 or less, 4.75 or less in the order of numericalvalues of the CD_(nominal) as listed above.

In order to set the leakage loss to the coating at the wavelength of1360 nm to 0.01 dB/km or less and to set the parallel propagation XTafter the propagation for 10 km to −20 dB or less, MFD/λ_(cc) ispreferably 9.81 or less, 9.28 or less, 8.76 or less, 8.23 or less, 7.70or less, 7.17 or less, 6.65 or less, 6.12 or less, 5.59 or less, or 5.07or less in the order of the numerical values of the CD_(nominal) aslisted above, and MFD/λ_(cc) is more preferably 9.15 or less, 8.62 orless, 8.10 or less, 7.57 or less, 7.04 or less, 6.52 or less, 5.99 orless, 5.46 or less, 4.94 or less, or 4.41 or less in the order of thenumerical values of the CD_(nominal) as listed above.

In order to set the leakage loss to the coating at the wavelength of1550 nm to 0.01 dB/km or less and to set the counter propagation XTafter the propagation for 10 km to −20 dB or less, MFD/λ_(cc) ispreferably 8.02 or less, 7.62 or less, 7.22 or less, 6.82 or less, 6.42or less, 6.03 or less, 5.63 or less, 5.23 or less, 4.83 or less, or 4.43or less in the order of the numerical values of the CD_(nominal) aslisted above, and MFD/λ_(cc) is more preferably 7.26 or less, 6.86 orless, 6.47 or less, 6.07 or less, 5.67 or less, 5.27 or less, 4.87 orless, 4.48 or less, 4.08 or less, or 3.68 or less in the order of thenumerical values of the CD_(nominal) as listed above.

In order to set the leakage loss to the coating at the wavelength of1550 nm to 0.01 dB/km or less and to set the parallel propagation XTafter the propagation for 10 km to −20 dB or less, MFD/λ_(cc) ispreferably 7.55 or less, 7.18 or less, 6.80 or less, 6.42 or less, 6.05or less, 5.67 or less, 5.30 or less, 4.92 or less, 4.55 or less, or 4.17or less in the order of the numerical values of the CD_(nominal) aslisted above, and MFD/λ_(cc) is more preferably 6.82 or less, 6.45 orless, 6.07 or less, 5.69 or less, 5.32 or less, 4.94 or less, 4.57 orless, 4.19 or less, 3.82 or less, or 3.44 or less in the order of thenumerical values of the CD_(nominal) as listed above.

FIG. 11 is a graph illustrating a relationship between the CD (theallowable minimum cladding diameter) and MFD/λ_(cc) of a case where amargin of 1 μm is added to d_(coat) and the margin of 1 μm is added toA, when the leakage loss to the coating is 0.01 dB/km, under a conditionthat the counter propagation XT after the propagation for 10 km(corresponding to the fiber length of 10 km) of the four-core MCF is −40dB (=−40 dB/10 km) and the parallel propagation XT after the propagationfor 10 km (corresponding to the fiber length of 10 km) is −40 dB (=−40dB/10 km), at both the wavelength of 1550 nm and the wavelength of 1360nm.

Note that in FIG. 11, the above-described relationships are illustratedsuch that a symbol “∘” represents the parallel propagation XT at thewavelength of 1550 nm, a symbol “● (indicated by hatching in FIG. 11)”represents the parallel propagation XT at the wavelength of 1360 nm, asymbol “□” represents the counter propagation XT at the wavelength of1550 nm, and a symbol “▪ (indicated by hatching in FIG. 11)” representsthe counter propagation XT at the wavelength of 1360 nm.

Although no dotted line is illustrated in FIG. 11, in a similar mannerto the case of FIG. 5 or the like, in order to set the leakage loss tothe coating at the wavelength of 1360 nm to 0.01 dB/km or less and toset the counter propagation XT after the propagation for 10 km to −40 dBor less, in consideration of the tolerance in the dimensions of the coreposition and the cladding diameter, the relationship betweenCD_(nominal) and MFD/λ_(cc) preferably satisfies at least one of thefollowing Formula (128) and Formula (129):

CD _(nominal)≥9.37MFD/λ_(cc)+31.73  (128); and

MFD/λ_(cc)≤0.1068CD _(nominal)−3.388  (129),

and more preferably satisfies at least one of the following Formula(130) and Formula (131):

CD _(nominal)≥9.37MFD/λ_(cc)+38.00  (130); and

MFD/λ_(cc)≤0.1068CD _(nominal)−4.058  (131).

In order to set the leakage loss to the coating at the wavelength of1360 nm to 0.01 dB/km or less and to set the parallel propagation XTafter the propagation for 10 km to −40 dB or less, the relationshipbetween CD_(nominal) and MFD/λ_(cc) preferably satisfies at least one ofthe following Formula (132) and (133):

CD _(nominal)≥10.32MFD/λ_(cc)+33.11  (132); and

MFD/λ_(cc)≤0.09690CD _(nominal)−3.208  (133),

and more preferably satisfies at least one of the following Formula(134) and Formula (135):

CD _(nominal)≥10.32MFD/λ_(cc)+39.23  (134); and

MFD/λ_(cc)≤0.09690CD _(nominal)−3.802  (135).

In order to set the leakage loss to the coating at the wavelength of1550 nm to 0.01 dB/km or less and to set the counter propagation XTafter the propagation for 10 km to −40 dB or less, the relationshipbetween CD_(nominal) and MFD/λ_(cc) satisfies at least one of thefollowing Formula (136) and Formula (137):

CD _(nominal)≥13.14MFD/λ_(cc)+24.43  (136); and

MFD/λ_(cc)≤0.07610CD _(nominal)−1.859  (137),

and preferably satisfies at least one of the following Formula (138) andFormula (139):

CD _(nominal)≥13.14MFD/λ_(cc)+34.09  (138); and

MFD/λ_(cc)≤0.07610CD _(nominal)−2.594  (139).

In order to set the leakage loss to the coating at the wavelength of1550 nm to 0.01 dB/km or less and to set the parallel propagation XTafter the propagation for 10 km to −40 dB or less, the relationshipbetween CD_(nominal) and MFD/λ_(cc) satisfies at least one of thefollowing Formula (140) and Formula (141):

CD _(nominal)≥14.47MFD/λ_(cc)+24.73  (140); and

MFD/λ_(cc)≤0.06911CD _(nominal)−1.709  (141),

and preferably satisfies at least one of the following Formula (142) andFormula (143):

CD _(nominal)≥14.47MFD/λ_(cc)+34.08  (142); and

MFD/λ_(cc)≤0.06911CD _(nominal)−2.406  (143).

In the four-core MCF having the square core arrangement, in order to setthe leakage loss to the coating at the wavelength of 1360 nm to 0.01dB/km or less and to set the counter propagation XT after thepropagation for 10 km to −40 dB or less, in consideration of thetolerance in the dimensions of the core position and the claddingdiameter, in a case where CD_(nominal) is 125 μm, 120 μin, 115 μin, 110μin, 105 μm, 100 μm, 95 μm, 90 μm, 85 μm, and 80 μm, MFD/λ_(cc) ispreferably 9.96 or less, 9.42 or less, 8.89 or less, 8.36 or less, 7.82or less, 7.29 or less, 6.76 or less, 6.22 or less, 5.69 or less, or 5.15or less in the order of the numerical values of the CD_(nominal) aslisted above, and MFD/λ_(cc) is more preferably 9.29 or less, 8.76 orless, 8.22 or less, 7.69 or less, 7.15 or less, 6.62 or less, 6.09 orless, 5.55 or less, 5.02 or less, or 4.48 or less in the order of thenumerical values of the CD_(nominal) as listed above.

In order to set the leakage loss to the coating at the wavelength of1360 nm to 0.01 dB/km or less and to set the parallel propagation XTafter the propagation for 10 km to −40 dB or less, MFD/λ_(cc) ispreferably 8.90 or less, 8.42 or less, 7.94 or less, 7.45 or less, 6.97or less, 6.48 or less, 6.00 or less, 5.51 or less, 5.03 or less, or 4.54or less in the order of the numerical values of the CD_(nominal) aslisted above, and the MFD/λ_(cc) is more preferably 8.31 or less, 7.83or less, 7.34 or less, 6.86 or less, 6.37 or less, 5.89 or less, 5.40 orless, 4.92 or less, 4.43 or less, or 3.95 or less in the order of thenumerical values of the CD_(nominal) as listed above.

In order to set the leakage loss to the coating at the wavelength of1550 nm to 0.01 dB/km or less and to set the counter propagation XTafter the propagation for 10 km to −40 dB or less, the MFD/λ_(cc) ispreferably 7.65 or less, 7.27 or less, 6.89 or less, 6.51 or less, 6.13or less, 5.75 or less, 5.37 or less, 4.99 or less, 4.61 or less, or 4.23or less in the order of the numerical values of the CD_(nominal) aslisted above, and MFD/λ_(cc) is more preferably 6.92 or less, 6.54 orless, 6.16 or less, 5.78 or less, 5.40 or less, 5.02 or less, 4.64 orless, 4.25 or less, 3.87 or less, or 3.49 or less in the order of thenumerical values of the CD_(nominal) as listed above.

In order to set the leakage loss to the coating at the wavelength of1550 nm to 0.01 dB/km or less and to set the parallel propagation XTafter the propagation for 10 km to −40 dB or less, MFD/λ_(cc) ispreferably 6.93 or less, 6.58 or less, 6.24 or less, 5.89 or less, 5.55or less, 5.20 or less, 4.86 or less, 4.51 or less, 4.17 or less, or 3.82or less in the order of the numerical values of the CD_(nominal) aslisted above, and MFD/A, is more preferably 6.23 or less, 5.89 or less,5.54 or less, 5.20 or less, 4.85 or less, 4.51 or less, 4.16 or less,3.81 or less, 3.47 or less, or 3.12 or less in the order of thenumerical values of the CD_(nominal) as listed above.

λ_(cc) is preferably 1260 nm or less, because a single mode operation onthe O-band can be ensured. In this situation, by setting MFD/λ_(cc) to6.5 or more, λ_(cc) can be set to 1260 nm or less, even in a case wherethe MFD falls within a range of 8.2 μm or more and 9. 0 μm or less with8.6 μm used as a basis. By setting MFD/2 to 7.2 or more, a larger MFDcan be achieved, the splice loss between the MCFs can be reduced, andλ_(cc) can be sufficiently smaller than 1260 nm (λ_(cc) is 1.2 μm orless) (that is, a margin can be taken). In this case, for example, MFDfalls within a range of 8.8 μm or more and 9.6 μm or less with 9.2 μmused as a basis, and λ_(cc)≤1.23 μm and MFD/λ_(cc)≥>7.2 are satisfied.In these cases, MFD/λ_(cc) preferably takes a value between an upperlimit defined from CD_(nominal) described above and a lower limitdefined from a range of MFD and λ_(cc).

In consideration of mass production of the MCFs, it is sufficient if theMCF has a structure in which the tolerance of MFD/λ_(cc) is 1.0 or more,preferably 1.5 or more, more preferably 2.0 or more, and furtherpreferably 2.5 or more. Most preferably, the MCF has a structure inwhich the tolerance of MFD/λ_(cc) is 3.0 or more.

The MCF preferably has a structure that allows MFD/λ_(cc) to be 6.5 ormore and 7.5 or less. Furthermore, the MCF preferably has a structurethat allows MFD/λ_(cc) to be 6.5 or more and 8.0 or less, morepreferably has a structure that allows 6.5 or more and 8.5 or less, andfurther preferably has a structure that allows 6.5 or more and 9.0 orless. The MCF most preferably has a structure that allows MFD/λ_(cc) tobe 6.5 or more and 9.5 or less.

The MCF may have a structure that allows 7.2 or more and 8.2 or less ofMFD/λ_(cc). Furthermore, the MCF preferably has a structure that allowsMFD/λ_(cc) to be 7.2 or more and 8.7 or less, more preferably has astructure that allows 7.2 or more and 9.2 or less, and furtherpreferably has a structure that allows 7.2 or more and 9.7 or less. TheMCF most preferably has a structure that allows MFD/λ_(cc) to be 7.2 ormore and 10.2 or less.

In a case where λ_(cc) is more than 1260 nm and 1360 nm or less, in theconfiguration of FIG. 12 (a fiber that is not formed into a cable) ofITU-T G.650.1(March/2018), 20 in out of 22 in in a sample fiber is bentwith a bending radius of 140 mm or more, one spool of bending with aradius of 40 mm is added before and after the above 20 in segment, andP_(h) represents an intensity of the higher-order mode and P_(f)represents an intensity of the fundamental mode, when all modes areuniformly excited, a wavelength at which 10 log₁₀[P_(h)/(P_(f)+P_(h))]=0.1 dB is satisfied is measured as λ_(cc).However, in the MCF according to the present disclosure, a cutoffwavelength (λ_(cc)R) is preferably 1260 nm or less, when measured bybending the segment of 20 in out of 22 in in the sample fiber with aradius of 60 mm or more and 100 mm or less that has been changed.Accordingly, the single mode operation on the O-band after cableinstallation can be ensured. In addition, the length L_(sample) [m] ofthe sample fiber falls within a range of more than 22 in and 1000 in orless, L_(sample)−2 [m] is bent with a bending radius of 140 mm or more,and one spool of bending with a radius of 40 mm is added before andafter the above L_(sample)−2 [m] segment. The cutoff wavelength(λ_(cc)L) that has been measured is preferably 1260 nm or less.Accordingly, in the cable having a cable length L_(sample) [m], thesingle mode operation on the O-band can be ensured.

In each core of the MCF according to the present disclosure, a bendingloss at the wavelength of 1310 nm or more and 1360 nm or less ispreferably 0.15 dB/turn or less at a bending radius of 10 mm, and ismore preferably 0.02 dB/turn or less. Accordingly, also in a case wherethe MCF according to the present disclosure is formed in an ultra-highdensity cable of the intermittent-bonding ribbon type, an increase inloss after being formed into a cable can be suppressed.

In a case where an MCF cable that incorporates the MCF according to thepresent disclosure is linearly extended (at least a bending radius of 1in or more), an average bending radius of the MCF formed into the cableis preferably 0.14 in or less, and more preferably 0.10 in or less. Inaddition, regarding the MCF cable incorporating the MCF according to thepresent disclosure, an average bending radius of the MCF formed into thecable is preferably 0.14 in or more and 0.3 in or less. Accordingly, theXT can be reduced.

Further, regarding the MCF cable incorporating the MCF according to thepresent disclosure, the average bending radius of the MCF formed intothe cable is preferably 0.03 in or more, and more preferably 0.06 in ormore. Accordingly, a loss caused by bending can be reduced.

Furthermore, the MCF cable incorporating the MCF according to thepresent disclosure is preferably an intermittent-bonding ribbon cable.Accordingly, the intermittent-bonding ribbon that is flexible can beformed into the cable while being spirally twisted, and the MCF can beformed into a cable with a small bending radius, so that the XT can bereduced.

The MCF cable incorporating the MCF according to the present disclosureis preferably a ribbon slot type cable, and preferably includes atension member at the center of the slot member. Accordingly, thebending radius of the MCF becomes easily controllable, and the XT can bereduced. In addition, the provision of the tension member at the centerof the slot member enables the cable to be easily bent in any direction,and the cable laying work can be easily performed.

Regarding the MCF cable incorporating the MCF according to the presentdisclosure, a tension member is preferably provided inside a sheathwithout the provision of a slot member in a space inside the sheath.Accordingly, the space inside the sheath can be effectively used, andthe number of cores per cross-sectional area of the MCF cable can beincreased.

As described heretofore, according to the MCFs according to the presentdisclosure, sufficient manufacturing tolerance is ensured, massproductivity is excellent, and degradation of splice loss can besuppressed.

What is claimed is:
 1. A multi-core optical fiber comprising: four coresextending along a central axis; and a common cladding covering each ofthe four cores, wherein the four cores each have an adjacentrelationship with two cores of remaining cores, a center-to-centerinterval Λ between the cores having the adjacent relationship among thefour cores falls within a range of a value of Λ_(nominal)−0.9 μm or moreand a value of Λ_(nominal)+0.9 μm or less with a predeterminedcore-interval nominal value Λ_(nominal) used as a basis, an outerdiameter of the common cladding falls within a range of 124 μm or moreand 126 μm or less with 125 μm used as a basis, in each of the fourcores, a mode field diameter MFD at a wavelength of 1310 nm, a cablecutoff wavelength λ_(cc) measured on a 22 in length of fiber, and ashortest distance d_(coat) of distances from centers of the four coresto an outer periphery of the common cladding satisfy a relationship in afollowing Formula (1), in any of the four cores:d _(coat)≥2.88MFD/λ_(cc)+5.36  (1), in each of the four cores, the modefield diameter MFD falls within a range of a value of an MFD referencevalue−0.4 μm or more and a value of the MFD reference value+0.4 μm orless, with a value of 8.6 μm or more and 9.2 gm or less used as the MFDreference value, in each of the four cores, a zero-dispersion wavelengthfalls within a range of a value of a wavelength reference value−12 nm ormore and a value of the wavelength reference value+12 nm or less with avalue of 1312 nm or more and 1340 nm or less used as the wavelengthreference value, in each of the four cores, a dispersion slope at thezero-dispersion wavelength is 0.092 ps/(nm²·km) or less, in each of thefour cores, the cable cutoff wavelength λ_(cc) is 1260 nm or less,either a first condition or a second condition is satisfied and either athird condition or a fourth condition is satisfied, the first conditionis defined that each of the four cores is in direct contact with thecommon cladding, the second condition relates to each of the four cores,each of the four cores further including an optical cladding providedbetween each of the four cores and the common cladding, and is definedthat a relative refractive index difference Δ2 of the optical claddingwith respect to the common cladding satisfies a relationship that−0.1%≤Δ2≤0.1%, the third condition is defined that a crosstalk betweenthe cores having the adjacent relationship for a fiber length of 10 kmat a wavelength of 1360 nm is −10 dB or less, and in each of the fourcores, MFD/λ_(cc) and a center-to-center interval Λ_(a) between thecores having the adjacent relationship satisfy a following Formula (2):7.2≤MFD/λ_(cc)≤10.2≤0.443Λ_(a)−5.33  (2), and the fourth condition isdefined that the crosstalk between the cores having the adjacentrelationship for the fiber length of 10 km at the wavelength of 1360 nmis −20 dB or less, and in each of the four cores, MFD/λ_(cc) and thecenter-to-center interval Λ_(a) between the cores having the adjacentrelationship satisfy a following Formula (3):7.2≤MFD/λ_(cc)≤10.2≤0.392Λ_(a)−4.88  (3).
 2. A multi-core optical fibercomprising: four cores extending along a central axis; and a commoncladding covering each of the four cores, wherein the four cores eachhave an adjacent relationship with two cores of remaining cores, acenter-to-center interval Λ between the cores having the adjacentrelationship among the four cores falls within a range of a value ofΛ_(nominal)−0.9 μm or more and a value of Λ_(nominal)+0.9 μm or lesswith a predetermined core-interval nominal value Λ_(nominal) used as abasis, a diameter CD of the common cladding falls within a range of avalue of CD_(nominal)−1 μm or more and a value of CD_(nominal)+1 μm orless with a predetermined cladding diameter nominal value CD_(nominal)[μm] of less than 125 μm used as a basis, in each of the four cores, amode field diameter MFD at a wavelength of 1310 nm, a cable cutoffwavelength λ_(cc) measured on a 22 in length of fiber, and a shortestdistance d_(coat) of distances from centers of the four cores to anouter periphery of the common cladding satisfy a following Formula (4),in any of the four cores:d _(coat)≥2.88MFD/λ_(cc)+5.36  (4), in each of the four cores, the modefield diameter MFD falls within a range of a value of an MFD referencevalue−0.4 μm or more and a value of the MFD reference value+0.4 μm orless with a value of 8.6 μm or more and 9.2 μm or less used as the MFDreference value, in each of the four cores, a zero-dispersion wavelengthfalls within a range of a value a wavelength reference value−12 nm ormore and a value of the wavelength reference value+12 nm or less with avalue of 1312 nm or more and 1340 nm or less used as the wavelengthreference value, in each of the four cores, a dispersion slope at thezero-dispersion wavelength is 0.092 ps/(nm²·km) or less, in each of thefour cores, the cable cutoff wavelength λ_(cc) is 1260 nm or less,either a first condition or a second condition is satisfied and either afifth condition or a sixth condition is satisfied, the first conditionis defined that each of the four cores is in direct contact with thecommon cladding, the second condition relates to each of the four cores,each of the four cores further including an optical cladding providedbetween each of the four cores and the common cladding, and is definedthat a relative refractive index difference Δ2 of the optical claddingwith respect to the common cladding satisfies a relationship that−0.1%≤Δ2≤0.1%, the fifth condition is defined that a crosstalk betweenthe cores having the adjacent relationship for a fiber length of 10 kmat a wavelength of 1360 nm is −10 dB or less, in each of the four cores,a following Formula (5):CD _(nominal)>13.31MFD/λ_(cc)+24.47  (5) is satisfied, and in each ofthe four cores, MFD/λ_(cc) and a center-to-center interval Λ_(a) betweenthe cores having the adjacent relationship satisfy a following Formula(6):6.5≤MFD/λ_(cc)≤9.5≤0.443Λ_(a)−5.33  (6), and the sixth condition isdefined that the crosstalk between the cores having the adjacentrelationship for the fiber length of 10 km at the wavelength of 1360 nmis −20 dB or less, in each of the four cores, a following Formula (7):CD _(nominal)≥9.37MFD/λ_(cc)+31.73  (7) is satisfied, and in each of thefour cores, MFD/λ_(cc) and the center-to-center interval Λ_(a) betweenthe cores having the adjacent relationship satisfy a following Formula(8):6.5MFDλ_(cc)≤9.5≤0.392Λ_(a)−4.88  (8).
 3. The multi-core optical fiberaccording to claim 1, further comprising a coating surrounding thecommon cladding, wherein a leakage loss from at least any of the fourcores to the coating at a wavelength of 1550 nm or a wavelength of 1625nm is 0.05 dB/km or more, a transmission loss of at least one of thefour cores at the wavelength of 1550 nm is 0.25 dB/km or more, or atransmission loss at the wavelength of 1625 nm is 0.25 dB/km or more. 4.The multi-core optical fiber according to claim 2, further comprising acoating surrounding the common cladding, wherein a leakage loss from atleast any of the four cores to the coating at a wavelength of 1550 nm ora wavelength of 1625 nm is 0.05 dB/km or more, a transmission loss of atleast one of the four cores at the wavelength of 1550 nm is 0.25 dB/kmor more, or a transmission loss at the wavelength of 1625 nm is 0.25dB/km or more.
 5. The multi-core optical fiber according to claim 1,wherein the third condition is satisfied, and the crosstalk between thecores having the adjacent relationship at a wavelength of 1550 nm forthe fiber length of 10 km is −10 dB or more.
 6. The multi-core opticalfiber according to claim 1, wherein the fourth condition is satisfied,and the crosstalk between the cores having the adjacent relationship ata wavelength of 1550 nm for the fiber length of 10 km is −20 dB or more.7. The multi-core optical fiber according to claim 2, wherein the fifthcondition is satisfied, and the crosstalk between the cores having theadjacent relationship at a wavelength of 1550 nm for the fiber length of10 km is −10 dB or more.
 8. The multi-core optical fiber according toclaim 2, wherein the sixth condition is satisfied, and the crosstalkbetween the cores having the adjacent relationship at a wavelength of1550 nm for the fiber length of 10 km is −20 dB or more.
 9. A multi-coreoptical fiber cable comprising a plurality of multi-core optical fibersincluding the multi-core optical fiber defined in claim
 1. 10. Themulti-core optical fiber cable according to claim 9, wherein themulti-core optical fiber has an average bending radius of 0.03 in ormore and 0.14 in or less, or 0.14 in or more and 0.3 in or less in afiber longitudinal direction.
 11. A multi-core optical fiber cablecomprising a plurality of multi-core optical fibers including themulti-core optical fiber defined in claim
 2. 12. The multi-core opticalfiber cable according to claim 11, wherein the multi-core optical fiberhas an average bending radius of 0.03 in or more and 0.14 in or less, or0.14 in or more and 0.3 in or less in a fiber longitudinal direction.13. A multi-core optical fiber cable incorporating a multi-core opticalfiber ribbon in which a plurality of multi-core optical fibers includingthe multi-core optical fiber defined in claim 1 are intermittentlybonded.
 14. The multi-core optical fiber cable according to claim 13,wherein the multi-core optical fiber ribbon is incorporated withspirally twisted.
 15. The multi-core optical fiber cable according toclaim 13, wherein the multi-core optical fiber has an average bendingradius of 0.03 in or more and 0.14 in or less, or 0.14 in or more and0.3 in or less in a fiber longitudinal direction.
 16. A multi-coreoptical fiber cable incorporating a multi-core optical fiber ribbon inwhich a plurality of multi-core optical fibers including the multi-coreoptical fiber defined in claim 2 are intermittently bonded.
 17. Themulti-core optical fiber cable according to claim 16, wherein themulti-core optical fiber ribbon is incorporated with spirally twisted.18. The multi-core optical fiber cable according to claim 16, whereinthe multi-core optical fiber has an average bending radius of 0.03 in ormore and 0.14 in or less, or 0.14 in or more and 0.3 in or less in afiber longitudinal direction.